Relevant bibliographies by topics / Hamiltonian PDE's

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Hamiltonian PDE's'

Author: Grafiati
Published: 4 June 2021
Last updated: 31 January 2023

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Journal articles on the topic "Hamiltonian PDE's"

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Rousset, Frederic, and Nikolay Tzvetkov. "Transverse nonlinear instability of solitary waves for some Hamiltonian PDE's." Journal de Mathématiques Pures et Appliquées 90, no. 6 (December 2008): 550–90. http://dx.doi.org/10.1016/j.matpur.2008.07.004.

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Kuksin, Sergej B. "Infinite-dimensional symplectic capacities and a squeezing theorem for Hamiltonian PDE's." Communications in Mathematical Physics 167, no. 3 (February 1995): 531–52. http://dx.doi.org/10.1007/bf02101534.

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Dubrovin, B. "Hamiltonian PDEs: deformations, integrability, solutions." Journal of Physics A: Mathematical and Theoretical 43, no. 43 (October 12, 2010): 434002. http://dx.doi.org/10.1088/1751-8113/43/43/434002.

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Dubrovin, Boris A. "Hamiltonian PDEs and Frobenius manifolds." Russian Mathematical Surveys 63, no. 6 (December 31, 2008): 999–1010. http://dx.doi.org/10.1070/rm2008v063n06abeh004575.

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Bridges, Thomas J., and Sebastian Reich. "Numerical methods for Hamiltonian PDEs." Journal of Physics A: Mathematical and General 39, no. 19 (April 24, 2006): 5287–320. http://dx.doi.org/10.1088/0305-4470/39/19/s02.

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Brugnano, Luigi, Gianluca Frasca-Caccia, and Felice Iavernaro. "Line Integral Solution of Hamiltonian PDEs." Mathematics 7, no. 3 (March 18, 2019): 275. http://dx.doi.org/10.3390/math7030275.

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In this paper, we report on recent findings in the numerical solution of Hamiltonian Partial Differential Equations (PDEs) by using energy-conserving line integral methods in the Hamiltonian Boundary Value Methods (HBVMs) class. In particular, we consider the semilinear wave equation, the nonlinear Schrödinger equation, and the Korteweg–de Vries equation, to illustrate the main features of this novel approach.
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Oh, Tadahiro, and Jeremy Quastel. "On the Cameron–Martin theorem and almost-sure global existence." Proceedings of the Edinburgh Mathematical Society 59, no. 2 (December 17, 2015): 483–501. http://dx.doi.org/10.1017/s0013091515000218.

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AbstractIn this paper we discuss various aspects of invariant measures for nonlinear Hamiltonian partial differential equations (PDEs). In particular, we show almost-sure global existence for some Hamiltonian PDEs with initial data of the form ‘a smooth deterministic function + a rough random perturbation’ as a corollary to the Cameron–Martin theorem and known almost-sure global existence results with respect to Gaussian measures on spaces of functions.
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Bambusi, D., and C. Bardelle. "Invariant tori for commuting Hamiltonian PDEs." Journal of Differential Equations 246, no. 6 (March 2009): 2484–505. http://dx.doi.org/10.1016/j.jde.2008.12.002.

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Gong, Yuezheng, and Yushun Wang. "An Energy-Preserving Wavelet Collocation Method for General Multi-Symplectic Formulations of Hamiltonian PDEs." Communications in Computational Physics 20, no. 5 (November 2016): 1313–39. http://dx.doi.org/10.4208/cicp.231014.110416a.

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AbstractIn this paper, we develop a novel energy-preserving wavelet collocation method for solving general multi-symplectic formulations of Hamiltonian PDEs. Based on the autocorrelation functions of Daubechies compactly supported scaling functions, the wavelet collocation method is conducted for spatial discretization. The obtained semi-discrete system is shown to be a finite-dimensional Hamiltonian system, which has an energy conservation law. Then, the average vector field method is used for time integration, which leads to an energy-preserving method for multi-symplectic Hamiltonian PDEs. The proposed method is illustrated by the nonlinear Schrödinger equation and the Camassa-Holm equation. Since differentiation matrix obtained by the wavelet collocation method is a cyclic matrix, we can apply Fast Fourier transform to solve equations in numerical calculation. Numerical experiments show the high accuracy, effectiveness and conservation properties of the proposed method.
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Moore, Brian E., and Sebastian Reich. "Multi-symplectic integration methods for Hamiltonian PDEs." Future Generation Computer Systems 19, no. 3 (April 2003): 395–402. http://dx.doi.org/10.1016/s0167-739x(02)00166-8.

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Dissertations / Theses on the topic "Hamiltonian PDE's"

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Khayamian, Chiara. "Periodic and Quasi-Periodic Solutions of some Non-Linear Hamiltonian PDE's." Thesis, Avignon, 2017. http://www.theses.fr/2017AVIG0418/document.

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Les équations aux dérivées partielles (EDP) permettent d’aborder d’un point de vue mathématique des phénomènes observés dans tous les domaines des sciences. Certaines EDP non-linéaires modélisent des problèmes de mécanique statistique, mécanique des fluides, théories de la gravitation ou des mathématiques financières.L’objectif de ce travail de thèse est l’étude de certains problèmes d’ EDP non-linéaires et hamiltoniennes et la recherche des leurs solutions périodiques et quasi-périodiques
The aim of this thesis is the research of periodic and quasi-periodic solutions for some non-linear hamiltonian PDEs
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Martin, Stephan [Verfasser]. "Applied Kinetic PDEs: Collective behavior models and Hamiltonian energy dynamics / Stephan Martin." München : Verlag Dr. Hut, 2012. http://d-nb.info/1025821270/34.

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Stoilov, Nikola. "Hamiltonian systems of hydrodynamic type in 2 + 1 dimensions and their dispersive deformations." Thesis, Loughborough University, 2011. https://dspace.lboro.ac.uk/2134/10183.

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Hamiltonian systems of hydrodynamic type occur in a wide range of applications including fluid dynamics, the Whitham averaging procedure and the theory of Frobenius manifolds. In 1 + 1 dimensions, the requirement of the integrability of such systems by the generalised hodograph transform implies that integrable Hamiltonians depend on a certain number of arbitrary functions of two variables. On the contrary, in 2 + 1 dimensions the requirement of the integrability by the method of hydrodynamic reductions, which is a natural analogue of the generalised hodograph transform in higher dimensions, leads to finite-dimensional moduli spaces of integrable Hamiltonians. We classify integrable two-component Hamiltonian systems of hydrodynamic type for all existing classes of differential-geometric Poisson brackets in 2D, establishing a parametrisation of integrable Hamiltonians via elliptic/hypergeometric functions. Our approach is based on the Godunov-type representation of Hamiltonian systems, and utilises a novel construction of Godunov's systems in terms of generalised hypergeometric functions. Furthermore, we develop a theory of integrable dispersive deformations of these Hamiltonian systems following a scheme similar to that proposed by Dubrovin and his collaborators in 1 + 1 dimensions. Our results show that the multi-dimensional situation is far more rigid, and generic Hamiltonians are not deformable. As an illustration we discuss a particular class of two-component Hamiltonian systems, establishing triviality of first order deformations and classifying Hamiltonians possessing nontrivial deformations of the second order.
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Bustillo, Jaime. "Rigidité symplectique et EDPs hamiltoniennes." Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLEE050/document.

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On étudie les propriétés de rigidité symplectique des difféomorphismes hamiltoniens en dimension finie et en dimension infinie. En dimension finie, les outils principaux qu'on utilise sont les fonctions génératrices et les capacités symplectiques. En dimension infinie on regarde les flots des équations en dérivées partielles (EDPs) hamiltoniennes et, en particulier, les flots qui peuvent être approchés uniformément par des flots hamiltoniens de dimension finie.Dans la première partie de la thèse on étudie les sélecteurs d'action définies à partir des fonctions génératrices et on construit des invariants hamiltoniens pour les sous-ensembles de $R^{2m}times T^*T^k$. Cela nous permet de démontrer un théorème non-squeezing coisotrope pour les difféomorphismes hamiltoniens à support compact de $R^{2n}$. On montre à continuation que cette propriété apparaisse dans certains cas non compacts. Finalement, on explique comment ce résultat donne aussi l'information sur le problème de rigidité symplectique en dimension intermédiaire. Encore en dimension finie, on démontre qu'on peut utiliser le théorème du chameau symplectique pour produire des sous-ensembles invariants compacts dans des surfaces d'energie.Dans la deuxième partie on étudie les propriétés de rigidité symplectique des flots des EDPs hamiltoniennes. On se place dans le contexte introduit par Kuksin et on étudie une classe particulière de EDPs semi-linéaires qui peuvent être approchées par flots hamiltoniens de dimension finie. D'abord on donne une nouvelle construction de capacité symplectique en dimension infinie à partir des capacités de Viterbo. Puis on démontre l'analogue de la rigidité intermédiaire pour certaines EDPs hamiltoniennes. Cette classe inclue l'équation d'ondes en dimension 1 avec une non-linéarité bornée, comme par exemple l'équation de Sine-Gordon. Dans la dernière partie de la thèse on s'intéresse à un analogue de la conjecture d'Arnold pour l'équation de Schrödinger périodique avec une non linéarité de convolution
We study symplectic rigidity properties in both finite and infinite dimension. In finite dimension, the main tools that we use are generating functions and symplectic capacities. In infinite dimension we study flows of Hamiltonian partial differential equations (PDEs) and, in particular, flows which can be uniformly approximated by finite dimensional Hamiltonian diffeomorphisms.In the first part of this thesis we study the action selectors defined from generating functions and we build Hamiltonian invariants for subsets of $R^{2m}times T^*T^k$. This allows us to prove a coisotropic non-squeezing theorem for compactly supported Hamiltonian diffeomorphisms of $R^{2n}$. We then extend this result to some non-compact settings. Finally we explain how this result can give information about the middle dimensional symplectic rigidity problem. Still in finite dimensions, we show that it is possible to use the symplectic camel theorem to create energy surfaces with compact invariant subsets.In the second part of the thesis we study symplectic rigidity properties of flows of Hamiltonian PDEs. We work in the context introduced by Kuksin and study a particular class of semi-linear Hamiltonian PDEs that can be approximated by finite dimensional Hamiltonian diffeomorphisms. We first give a new construction of an infinite dimensional capacity using Viterbo's capacities. The main result of this part is the proof of the analogue of the middle dimensional rigidity for certain types of Hamiltonian PDEs. These include nonlinear string equations with bounded nonlinearity such as the Sine-Gordon equation. In the final part of this thesis we study an analogue of Arnold's conjecture for the periodic Schrödinger equations with a convolution nonlinearity
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Thomann, Laurent. "Dynamiques hamiltoniennes et aléa." Habilitation à diriger des recherches, Université de Nantes, 2013. http://tel.archives-ouvertes.fr/tel-00906186.

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À l'aide de méthodes probabilistes, nous donnons des propriétés qualitatives de solutions d'équations aux dérivées partielles de type Schrödinger ou ondes. Nous tirons profit de l'aléa grâce à des propriétés de régularisation de séries aléatoires ou en éliminant un certain nombre de mauvaises valeurs d'un paramètre de l'équation. Ainsi, nous obtenons, sur un gros ensemble de paramètres, des résultats concernant la dynamique de l'équation. Notons que physiquement cette approche a un sens puisque les paramètres et les conditions initiales de l'équation ne peuvent être déterminés de façon absolue. De plus, dans chacune de nos méthodes employées, nous obtenons des résultats de stabilité de la dynamique par rapport aux conditions initiales. Enfin, nous montrons que l'approche précédente est pertinente en construisant, pour des choix particuliers de paramètres, des trajectoires exceptionnelles en utilisant des phénomènes de résonance.
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Jézéquel, Tiphaine. "Formes normales de champs de vecteurs : restes exponentiellement petits dans le cas non autonome périodique et orbites homoclines à plusieurs boucles au voisinage de la résonance 0²iw hamiltonienne." Phd thesis, Université Paul Sabatier - Toulouse III, 2011. http://tel.archives-ouvertes.fr/tel-00649382.

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Dans cette thèse on s'intéresse à deux problèmes faisant intervenir des formes normales de champs de vecteurs et des phénomènes exponentiellement petits. Dans le premier chapitre on démontre tout d'abord deux théorèmes de normalisation avec restes exponentiellement petits pour des champs de vecteurs analytiques au voisinage d'un point d'équilibre, dans le cas non autonome périodique. Le premier théorème de normalisation permet de construire une quasi-variété invariante à un exponentiellement petit près, tandis que le deuxième met le champ de vecteur sous la forme normale de Elphick-Tirapegui-Brachet-Coullet-Iooss à un exponentiellement petit près. Dans le deuxième chapitre on travaille près d'un point d'équilibre d'une famille de systèmes hamiltoniens au voisinage d'une résonance 0²iw. On démontre l'existence d'une famille d'orbites périodiques entourant l'équilibre puis l'existence d'orbites homoclines à plusieurs boucles à chacune de ces orbites périodiques, aussi proche de cet équilibre que l'on veut à l'exception de l'équilibre lui-même. La démonstration est basée sur la preuve d'un théorème de forme normale hamiltonien inspiré des formes normales de Elphick-Tirapegui-Brachet-Coullet-Iooss ainsi que sur une normalisation locale hamiltonienne s'appuyant sur un résultat de Moser. On obtient ensuite le résultat grâce à des arguments géométriques liés à la petite dimension et à un théorème KAM qui permet de confiner les boucles. Pour le même problème dans le cadre d'un champ de vecteurs réversible non hamiltonien, l'apparition d'exponentiellement petits lors de la perturbation de l'orbite homocline de la forme normale empêche la démonstration de l'existence d'orbites homoclines à des orbites périodiques de taille exponentiellement petite. Le même phénomène apparait ici mais l'obstacle est contourné grâce à des arguments géométriques spécifiques aux système Hamiltoniens.
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Guelmame, Billel. "Sur une régularisation hamiltonienne et la régularité des solutions entropiques de certaines équations hyperboliques non linéaires." Thesis, Université Côte d'Azur, 2020. https://tel.archives-ouvertes.fr/tel-03177654.

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Dans cette thèse, nous étudions certaines régularisations conservatives et non dispersives pour des lois de conservation. Ces régularisations sont obtenues en s’inspirant de celle du système de Saint-Venant introduite par Clamond et Dutykh. Nous étudions également la régularité, dans des espaces BV généralisés, des solutions entropiques de certaines équations hyperboliques non linéaires. Dans la première partie, nous obtenons et étudions une régularisation appropriée de l’équation de Burgers inviscide, ainsi que sa généralisation aux lois de conservation scalaires. Nous prouvons que cette généralisation est localement bien posée pour les solutions régulières. Nous montrons aussi l’existence globale des solutions qui satisfont une inégalité d’Oleinik pour des flux uniformément convexes. Lorsque le paramètre de régularisation ``l’’ tend vers zéro, nous prouvons que ces solutions convergent, pour une sous-suite, vers les solutions de la loi de conservation scalaire originale, au moins pour un petit intervalle de temps.Nous généralisons également les équations Saint-Venant régularisées afin d’obtenir une régularisation du système d’Euler barotrope, ainsi qu’une régularisation du système de Saint-Venant avec fond variable. Nous montrons que ces deux systèmes sont bien posés localement dans Hs, avec s≥2. Dans la deuxième partie, nous démontrons un effet régularisant, sur les conditions initiales, des lois de conservation scalaires pour un flux lipschitzien strictement convexe, ainsi que pour des équations scalaires avec un terme source linéaire. Dans certains cas, nous donnons une borne de l’effet régularisant. Enfin, nous prouvons l’existence globale des solutions entropiques d’une classe de système triangulaire ayant une équation de transport dans BV^s x L^∞ où s > 1/3
In this thesis, we study some non-dispersive conservative regularisations for the scalar conservation laws and also for the barotropic Euler system. Those regularisations are obtained inspired by a regularised Saint-Venant system introduced by Clamond and Dutykh in 2017. We also study the regularity, in generalised BV spaces, of the entropy solutions of some nonlinear hyperbolic equations. In the first part, we obtain and study a suitable regularisation of the inviscid Burgers equation, as well as its generalisation to scalar conservation laws. We prove that this regularisation is locally well-posedness for smooth solutions. We also prove the global existence of solutions that satisfy a one-sided Oleinik inequality for uniformly convex fluxes. When the regularising parameter ``l’’ goes to zero, we prove that the solutions converge, up to a subsequence, to the solutions of the original scalar conservation law, at least for a short time. We also generalise the regularised Saint-Venant equations to obtain a regularisation of the barotropic Euler system, and the Saint-Venant system with uneven bottom. We prove that both systems are locally well-posed in Hs, with s ≥ 2. In the second part, we prove a regularising effect, on the initial data, of scalar conservation laws with Lipschitz strictly convex flux, and of scalar equations with a linear source term. For some cases, we give a limit of the regularising effect.Finally, we prove the global existence of entropy solutions of a class of triangular systems involving a transport equation in BV^s x L^∞ where s > 1/3
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Sierra, Nunez Jesus Alfredo. "A Study of Schrödinger–Type Equations Appearing in Bohmian Mechanics and in the Theory of Bose–Einstein Condensates." Diss., 2018. http://hdl.handle.net/10754/627883.

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The Schrödinger equations have had a profound impact on a wide range of fields of modern science, including quantum mechanics, superfluidity, geometrical optics, Bose-Einstein condensates, and the analysis of dispersive phenomena in the theory of PDE. The main purpose of this thesis is to explore two Schrödinger-type equations appearing in the so-called Bohmian formulation of quantum mechanics and in the study of exciton-polariton condensates. For the first topic, the linear Schrödinger equation is the starting point in the formulation of a phase-space model proposed in [1] for the Bohmian interpretation of quantum mechanics. We analyze this model, a nonlinear Vlasov-type equation, as a Hamiltonian system defined on an appropriate Poisson manifold built on Wasserstein spaces, the aim being to establish its existence theory. For this purpose, we employ results from the theory of PDE, optimal transportation, differential geometry and algebraic topology. The second topic of the thesis is the study of a nonlinear Schrödinger equation, called the complex Gross-Pitaevskii equation, appearing in the context of Bose-Einstein condensation of exciton-polaritons. This model can be roughly described as a driven-damped Gross-Pitaevskii equation which shares some similarities with the complex Ginzburg-Landau equation. The difficulties in the analysis of this equation stem from the fact that, unlike the complex Ginzburg-Landau equation, the complex Gross-Pitaevskii equation does not include a viscous dissipation term. Our approach to this equation will be in the framework of numerical computations, using two main tools: collocation methods and numerical continuation for the stationary solutions and a time-splitting spectral method for the dynamics. After performing a linear stability analysis on the computed stationary solutions, we are led to postulate the existence of radially symmetric stationary ground state solutions only for certain values of the parameters in the equation; these parameters represent the “strength” of the driving and damping terms. Moreover, numerical continuation allows us to show, for fixed parameters, the ground and some of the excited state solutions of this equation. Finally, for the values of the parameters that do not produce a stable radially symmetric solution, our dynamical computations show the emergence of rotating vortex lattices.
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Ussembayev, Nail. "Nonlinear Wave Motion in Viscoelasticity and Free Surface Flows." Diss., 2020. http://hdl.handle.net/10754/664399.

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This dissertation revolves around various mathematical aspects of nonlinear wave motion in viscoelasticity and free surface flows. The introduction is devoted to the physical derivation of the stress-strain constitutive relations from the first principles of Newtonian mechanics and is accessible to a broad audience. This derivation is not necessary for the analysis carried out in the rest of the thesis, however, is very useful to connect the different-looking partial differential equations (PDEs) investigated in each subsequent chapter. In the second chapter we investigate a multi-dimensional scalar wave equation with memory for the motion of a viscoelastic material described by the most general linear constitutive law between the stress, strain and their rates of change. The model equation is rewritten as a system of first-order linear PDEs with relaxation and the well-posedness of the Cauchy problem is established. In the third chapter we consider the Euler equations describing the evolution of a perfect, incompressible, irrotational fluid with a free surface. We focus on the Hamiltonian description of surface waves and obtain a recursion relation which allows to expand the Hamiltonian in powers of wave steepness valid to arbitrary order and in any dimension. In the case of pure gravity waves in a two-dimensional flow there exists a symplectic coordinate transformation that eliminates all cubic terms and puts the Hamiltonian in a Birkhoff normal form up to order four due to the unexpected cancellation of the coefficients of all fourth order non-generic resonant terms. We explain how to obtain higher-order vanishing coefficients. Finally, using the properties of the expansion kernels we derive a set of nonlinear evolution equations for unidirectional gravity waves propagating on the surface of an ideal fluid of infinite depth and show that they admit an exact traveling wave solution expressed in terms of Lambert’s W-function. The only other known deep fluid surface waves are the Gerstner and Stokes waves, with the former being exact but rotational whereas the latter being approximate and irrotational. Our results yield a wave that is both exact and irrotational, however, unlike Gerstner and Stokes waves, it is complex-valued.
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Books on the topic "Hamiltonian PDE's"

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Giancarlo, Benettin, Henrard J, Kuksin Sergej B. 1955-, Giorgilli Antonio, Centro internazionale matematico estivo, and European Mathematical Society, eds. Hamiltonian dynamics theory and applications: Lectures given at the C.I.M.E.-E.M.S. Summer School, held in Cetraro, Italy, July 1-10, 1999. Berlin: Springer, 2005.

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Analysis of Hamiltonian PDEs. Oxford: Oxford University Press, 2000.

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Nonlinear oscillations of Hamiltonian PDEs. Boston: Birkhauser, 2007.

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Berti, Massimiliano. Nonlinear Oscillations of Hamiltonian PDEs. Boston, MA: Birkhäuser Boston, 2007. http://dx.doi.org/10.1007/978-0-8176-4681-3.

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Dzhamay, Anton, Christopher W. Curtis, Willy A. Hereman, and B. Prinari. Nonlinear wave equations: Analytic and computational techniques : AMS Special Session, Nonlinear Waves and Integrable Systems : April 13-14, 2013, University of Colorado, Boulder, CO. Providence, Rhode Island: American Mathematical Society, 2015.

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Benettin, Giancarlo, Jacques Henrard, Sergej B. Kuksin, and Antonio Giorgilli. Hamiltonian Dynamics - Theory and Applications: Lectures Given at the C. I. M. E. Summer School Held in Cetraro, Italy, July 1-10 1999. Springer London, Limited, 2010.

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Henrard, Jacques, Giancarlo Benettin, and Sergei Kuksin. Hamiltonian Dynamics - Theory and Applications: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 1-10, 1999 (Lecture Notes in Mathematics / Fondazione C.I.M.E., Firenze). Springer, 2005.

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Berti, Massimiliano. Nonlinear Oscillations of Hamiltonian PDEs. Springer, 2008.

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Lin, Zhiwu, and Chongchun Zeng. Instability, Index Theorem, and Exponential Trichotomy for Linear Hamiltonian PDEs. American Mathematical Society, 2022.

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Nonlinear Oscillations of Hamiltonian PDEs (Progress in Nonlinear Differential Equations and Their Applications Book 74). Birkhäuser, 2007.

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Book chapters on the topic "Hamiltonian PDE's"

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Bourgain, J. "Problems in Hamiltonian PDE’S." In Visions in Mathematics, 32–56. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0422-2_2.

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Kersten, P., I. S. Krasil′shchik, A. M. Verbovetsky, and R. Vitolo. "Hamiltonian Structures for General PDEs." In Differential Equations - Geometry, Symmetries and Integrability, 187–98. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00873-3_9.

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Berti, Massimiliano. "A Tutorial in Nash–Moser Theory." In Nonlinear Oscillations of Hamiltonian PDEs, 59–71. Boston, MA: Birkhäuser Boston, 2007. http://dx.doi.org/10.1007/978-0-8176-4681-3_3.

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Berti, Massimiliano. "Forced Vibrations." In Nonlinear Oscillations of Hamiltonian PDEs, 111–37. Boston, MA: Birkhäuser Boston, 2007. http://dx.doi.org/10.1007/978-0-8176-4681-3_5.

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Kuksin, Sergei. "Lectures on Hamiltonian Methods in Nonlinear PDEs." In Lecture Notes in Mathematics, 143–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/978-3-540-31541-4_3.

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Melikyan, Arik. "Smooth Solutions of a PDE with Nonsmooth Hamiltonian." In Generalized Characteristics of First Order PDEs, 199–225. Boston, MA: Birkhäuser Boston, 1998. http://dx.doi.org/10.1007/978-1-4612-1758-9_7.

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Wu, Xinyuan, Kai Liu, and Wei Shi. "General Local Energy-Preserving Integrators for Multi-symplectic Hamiltonian PDEs." In Structure-Preserving Algorithms for Oscillatory Differential Equations II, 255–91. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-48156-1_12.

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Birindelli, Isabeau, Françoise Demengel, and Fabiana Leoni. "Dirichlet Problems for Fully Nonlinear Equations with “Subquadratic” Hamiltonians." In Contemporary Research in Elliptic PDEs and Related Topics, 107–27. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18921-1_2.

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Dubrovin, Boris. "Hamiltonian Perturbations of Hyperbolic PDEs: from Classification Results to the Properties of Solutions." In New Trends in Mathematical Physics, 231–76. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-2810-5_18.

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"Hamiltonian PDEs." In Simulating Hamiltonian Dynamics, 316–56. Cambridge University Press, 2005. http://dx.doi.org/10.1017/cbo9780511614118.013.

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Conference papers on the topic "Hamiltonian PDE's"

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Borja, Pablo, Rafael Cisneros, and Romeo Ortega. "Shaping the energy of port-Hamiltonian systems without solving PDE's." In 2015 54th IEEE Conference on Decision and Control (CDC). IEEE, 2015. http://dx.doi.org/10.1109/cdc.2015.7403116.

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BAMBUSI, DARIO. "Birkhoff normal form for some quasilinear Hamiltonian PDEs." In XIVth International Congress on Mathematical Physics. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812704016_0024.

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3

Brugnano, L., F. Iavernaro, J. I. Montijano, and L. Rández. "Space-time spectrally accurate HBVMs for Hamiltonian PDEs." In CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5114129.

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4

Brugnano, Luigi, Gianluca Frasca Caccia, and Felice Iavernaro. "Recent advances in the numerical solution of Hamiltonian PDEs." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912438.

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Brugnano, Luigi, Gianluca Frasca Caccia, and Felice Iavernaro. "Energy conservation issues in the numerical solution of Hamiltonian PDEs." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912306.

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6

Ramakrishnan, Narayanan, and N. Sri Namachchivaya. "Dynamics of Spinning Disc Parametrically Excited by Noise." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8099.

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Abstract:
Abstract The nonlinear dynamics of a circular spinning disc parametrically excited by noise of small intensity is investigated. The governing PDEs are reduced using a Galerkin reduction procedure to a two-DOF system of ODEs which, govern the transverse motion of the disc. The dynamics is simplified by exploiting the S1 invariance of the equations of motion of the reduced system and further, reduced by performing stochastic averaging. The resulting one-dimensional Markov diffusive process is studied in detail. The stationary probability density distribution is obtained by solving the Fokker-Planck equation along with the appropriate boundary conditions. The boundary behaviour is studied using an asymptotic approach. Some aspects of dynamical and phenomenological bifurcations of the stationary solution are also investigated. The scheme of things presented here can be applied in principle to a four-dimensional Hamiltonian system possessing one integral of motion in addition to the hamiltonian and having one fixed point.
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7

McEneaney, William M. "Curse-of-Dimensionality Free Method for Bellman PDEs with Semiconvex Hamiltonians." In Proceedings of the 45th IEEE Conference on Decision and Control. IEEE, 2006. http://dx.doi.org/10.1109/cdc.2006.377399.

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