Relevant bibliographies by topics / Nonlinear wave theories

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

Academic literature on the topic 'Nonlinear wave theories'

Author: Grafiati
Published: 28 June 2021
Last updated: 29 July 2025

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Journal articles on the topic "Nonlinear wave theories"

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Nigama Prasan Sahoo. "Investigating the Role of Nonlinearity in Plasma Wave Dynamics: Theoretical and Computational Perspectives." Advances in Nonlinear Variational Inequalities 28, no. 4s (2025): 366–79. https://doi.org/10.52783/anvi.v28.3338.

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Plasma waves are fundamental for understanding many plasma phenomena, and at high enough amplitudes, the wave can also become nonlinear and complex. Research on nonlinear dynamics of plasma waves is critical for many applications, including fusion energy, space physics and plasma engineering. Theoretical aspects of nonlinear plasma wave propagation: wave packets, solitons, modulation instability, and wave-particle interaction. We generalize the standard theories of plasma waves to include non-linear terms and discuss how these non-linear equations can be solved numerically. We further discuss
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Zhang, Huichen, and Markus Brühl. "GENERATION OF EXTREME TRANSIENT WAVES IN EXPERIMENTAL MODELS." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 51. http://dx.doi.org/10.9753/icce.v36.waves.51.

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The transfer of natural waves and sea states into small- and large-scale model teste contributes to the proper design of offshore and coastal structure. Such shallow-water ocean surface waves are highly nonlinear and subject to wave transformation and nonlinear wave-wave interactions. However, the standard methods of wave generation according to conventional wave theories and wave analysis methods are limited to simple regular waves, simple sea states and low-order wave generation without considering the nonlinear wave-wave interactions. The research project Generation of Extreme Transient Wav
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Johnson, R. S. "Edge waves: theories past and present." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 365, no. 1858 (2007): 2359–76. http://dx.doi.org/10.1098/rsta.2007.2013.

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The problem of edge waves as an example within classical water-wave theory is described by presenting an overview of some of the theories that have been offered for this phenomenon. The appropriate governing equations and boundary conditions are formulated, and then the important discoveries of Stokes and Ursell, concerning the travelling edge wave, are presented. (We do not address the corresponding problem of standing waves.) Thus, the linear problem and its spectrum are constructed; in addition, we also present the linear long-wave approximation to the problem, as well as Whitham's weakly n
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Hardy, Thomas A., and Nicholas C. Kraus. "COUPLING STOKES AND CNOIDAL WAVE THEORIES IN A NONLINEAR REFRACTION MODEL." Coastal Engineering Proceedings 1, no. 21 (1988): 42. http://dx.doi.org/10.9753/icce.v21.42.

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An efficient numerical model is presented for calculating the refraction and shoaling of finite-amplitude waves over an irregular sea bottom. The model uses third-order Stokes wave theory in relatively deep water and second-order cnoidal wave theory in relatively shallow water. It can also be run using combinations of lower-order wave theories, including a pure linear wave mode. The problem of the connection of Stokes and cnoidal theories is investigated, and it is found that the use of second-order rather than first-order cnoidal theory greatly reduces the connection discontinuity. Calculatio
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Eldrup, Mads Røge, and Thomas Lykke Andersen. "Applicability of Nonlinear Wavemaker Theory." Journal of Marine Science and Engineering 7, no. 1 (2019): 14. http://dx.doi.org/10.3390/jmse7010014.

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Generation of high-quality waves is essential when making numerical or physically model tests. When using a wavemaker theory outside the validity area, spurious waves are generated. In order to investigate the validity of different wave generation methods, new model test results are presented where linear and nonlinear wave generation theories are tested on regular and irregular waves. A simple modification to the second-order wavemaker theory is presented, which significantly reduces the generation of spurious waves when used outside its range of applicability. For highly nonlinear regular wa
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Vakakis, A. F. "Scattering of Structural Waves by Nonlinear Elastic Joints." Journal of Vibration and Acoustics 115, no. 4 (1993): 403–10. http://dx.doi.org/10.1115/1.2930364.

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An analytic study of the scattering of structural waves by nonlinear elastic joints is presented. Under the assumption of small nonlinearities and/or amplitudes of motion, an averaging methodology is implemented for analyzing the interaction between an incident wave and a nonlinear joint with symmetric stiffness. It is found that, contrary to the predictions of existing linear theories, a single incident wave gives rise to an infinity of reflected waves with frequencies equal to odd multiples of the frequency of the incident wave. The orders of magnitude of the amplitudes of the various reflec
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RAVAL, ASHISH, XIANYUN WEN, and MICHAEL H. SMITH. "Numerical simulation of viscous, nonlinear and progressive water waves." Journal of Fluid Mechanics 637 (September 23, 2009): 443–73. http://dx.doi.org/10.1017/s002211200999070x.

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A numerical simulation is performed to study the velocity, streamlines, vorticity and shear stress distributions in viscous water waves with different wave steepness in intermediate and deep water depth when the average wind velocity is zero. The numerical results present evidence of ‘clockwise’ and ‘anticlockwise’ rotation of the fluid at the trough and crest of the water waves. These results show thicker vorticity layers near the surface of water wave than that predicted by the theories of inviscid rotational flow and the low Reynolds number viscous flow. Moreover, the magnitude of vorticity
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Zimmerman, W. B., and J. M. Rees. "Long solitary internal waves in stable stratifications." Nonlinear Processes in Geophysics 11, no. 2 (2004): 165–80. http://dx.doi.org/10.5194/npg-11-165-2004.

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Abstract. Observations of internal solitary waves over an antarctic ice shelf (Rees and Rottman, 1994) demonstrate that even large amplitude disturbances have wavelengths that are bounded by simple heuristic arguments following from the Scorer parameter based on linear theory for wave trapping. Classical weak nonlinear theories that have been applied to stable stratifications all begin with perturbations of simple long waves, with corrections for weak nonlinearity and dispersion resulting in nonlinear wave equations (Korteweg-deVries (KdV) or Benjamin-Davis-Ono) that admit localized propagatin
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Sánchez-Garrido, J. C., and V. Vlasenko. "Long-term evolution of strongly nonlinear internal solitary waves in a rotating channel." Nonlinear Processes in Geophysics 16, no. 5 (2009): 587–98. http://dx.doi.org/10.5194/npg-16-587-2009.

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Abstract. The evolution of internal solitary waves (ISWs) propagating in a rotating channel is studied numerically in the framework of a fully-nonlinear, nonhydrostatic numerical model. The aim of modelling efforts was the investigation of strongly-nonlinear effects, which are beyond the applicability of weakly nonlinear theories. Results reveal that small-amplitude waves and sufficiently strong ISWs evolve differently under the action of rotation. At the first stage of evolution an initially two-dimensional ISW transforms according to the scenario described by the rotation modified Kadomtsev-
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Huang, Miaomiao, Yinghua Li, and Ziying Pan. "Numerical research on internal solitary waves in stratified fluid." Journal of Physics: Conference Series 2718, no. 1 (2024): 012007. http://dx.doi.org/10.1088/1742-6596/2718/1/012007.

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Abstract Internal solitary waves are a common nonlinear large amplitude internal wave in nature, which can cause strong divergence and sudden strong currents in seawater during propagation, thus having great destructive effects on marine structures. The paper focuses on numerical wave generation based on three types of internal solitary wave theories. The waves are numerical simulated by RANS method in the paper. The numerical results of internal solitary wave theories are compared and analyzed. It shows that under the same numerical water tank scale and calculation conditions, the mKdV theory
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Dissertations / Theses on the topic "Nonlinear wave theories"

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Girard, Réjean. "Relativistic nonlinear wave equations with groups of internal symmetry." Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75688.

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A nonlinear wave equation invariant with respect to unitary representations of the Lorentz group is considered in an attempt to describe extended particles with spin and positive definite energy by means of a self-confined classical field. The wave function has an infinite number of components and, in the specific representations used, the corresponding internal degree of freedom is identified with the spin. A fractional power of the scalar bilinear invariant appears as an appropriate choice for the nonlinearity in order that all the stationary states be localized. Two approximation methods ar
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Hoseini, Sayed Mohammad. "Solitary wave interaction and evolution." Access electronically, 2007. http://www.library.uow.edu.au/adt-NWU/public/adt-NWU20080221.110619/index.html.

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Kim, Won-Gyu 1962. "A Study of Nonlinear Dynamics in an Internal Water Wave Field in a Deep Ocean." Thesis, University of North Texas, 1996. https://digital.library.unt.edu/ark:/67531/metadc278092/.

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The Hamiltonian of a stably stratified incompressible fluid in an internal water wave in a deep ocean is constructed. Studying the ocean internal wave field with its full dynamics is formidable (or unsolvable) so we consider a test-wave Hamiltonian to study the dynamical and statistical properties of the internal water wave field in a deep ocean. Chaos is present in the internal test-wave dynamics using actual coupling coefficients. Moreover, there exists a certain separatrix net that fills the phase space and is covered by a thin stochastic layer for a two-triad pure resonant interaction. The
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Narisetti, Raj K. "Wave propagation in nonlinear periodic structures." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/39643.

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A periodic structure consists of spatially repeating unit cells. From man-made multi-span bridges to naturally occurring atomic lattices, periodic structures are ubiquitous. The periodicity can be exploited to generate frequency bands within which elastic wave propagation is impeded. A limitation to the linear periodic structure is that the filtering properties depend only on the structural design and periodicity which implies that the dispersion characteristics are fixed unless the overall structure or the periodicity is altered. The current research focuses on wave propagation in nonlinear
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Franz, David, and University of Lethbridge Faculty of Arts and Science. "Turing patterns in linear chemical reaction systems with nonlinear cross diffusion." Thesis, Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2007, 2007. http://hdl.handle.net/10133/659.

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Turing patterns have been studied for over 50 years as a pattern forming mechanism. To date the current focus has been on the reaction mechanism, with little to no emphasis on the diffusion terms. This work focuses on combining the simplest reaction mechanism possible and the use of nonlinear cross diffusion to form Turing patterns. We start by using two methods of bifurcation analysis to show that our model can form a Turing instability. A diffusion model (along with some variants) is then presented along with the results of numerical simulations. Various tests on both the numerical methods a
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Kuechler, Sebastian. "Wave Propagation in an Elastic Half-Space with Quadratic Nonlinearity." Thesis, Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19823.

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This study investigates wave propagation in an elastic half-space with quadratic nonlinearity due to a line load on the surface. The consideration of this problem is one of the well known Lamb problems. Even since Lamb's original solution, numerous investigators have obtained solutions to many different variants of the Lamb problem. However, most of the solutions existing in the current literature are limited to wave propagation in a linear elastic half-space. In this work, the Lamb problem in an elastic half-space with quadratic nonlinearity is considered. For this, the problem is first formu
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Kupčíková, Laura. "Částice plovoucí na volné hladině vln." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-444637.

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This master’s thesis deals with analytical and numerical description of surface gravity waves. Wave theories and their influence on water particle movement is described in the theoretical part of the thesis. Water particle moves in the same direction as wave propagation and this phenomenon is called Stokes drift. It has a significant influence on sediment transport and floating particle movement at water free surface. The experimental part consists of wave profile monitoring and water particle tracking in a wave flume with wave generator and beach model. The experimental results are compared w
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Braun, Michael Rainer. "Characterization of nonlinearity parameters in an elastic material with quadratic nonlinearity with a complex wave field." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26566.

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Thesis (M. S.)--Civil and Environmental Engineering, Georgia Institute of Technology, 2009.<br>Committee Chair: Jacobs, Laurence; Committee Co-Chair: Qu, Jianmin; Committee Member: DesRoches, Reginald. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Aceves, Alejandro Borbolla. "Snell's laws at the interface between nonlinear dielectrics." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/184467.

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A theory is presented which describes the global reflection and transmission characteristics of a self-focused channel propagating at an oblique angle of incidence to an interface separating two or more self-focusing nonlinear dielectric media. A complete characterization of the different behavior of the channel is given in the proper parameter space. In the dominant region, the nonlinear wavepacket representing the self-focused channel is represented as an equivalent particle moving in an equivalent potential. The dynamics of the particle is described by Newton's equations of motion, with the
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Ohm, Won-suk. "Effects of dispersion on nonlinear surface acoustic waves in substrates laminated with films /." Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3038194.

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Books on the topic "Nonlinear wave theories"

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Kichenassamy, Satyanad. Nonlinear wave equations. M. Dekker, 1996.

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Oskar, Mahrenholtz, and Markiewicz M, eds. Nonlinear water wave interaction. WIT Press, 1999.

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NATO Advanced Research Workshop on Nonlinear Wave Processes in Excitable Media (1989 Leeds, England). Nonlinear wave processes in excitable media. Plenum Press, 1991.

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Shen, Samuel S. A course on nonlinear waves. Springer, 1993.

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Toda, Morikazu. Nonlinear waves and solitons. Kluwer, 1989.

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Baumgartel, Klaus. Topics on nonlinear wave-plasma interaction. Birkhaüser Verlag, 1987.

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Baumgartel, Klaus. Topics on nonlinear wave-plasma interaction. Birkhauser Verlag, 1987.

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Engelbrecht, Jüri. Nonlinear Wave Dynamics: Complexity and Simplicity. Springer Netherlands, 1997.

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Bonilla, L. L. Nonlinear wave methods for charge transport. Wiley-VCH, 2010.

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Pornsuwancharoen, N. Optical solitons in nonlinear micro ring resonators: Unexpected results and applications. Nova Science Publishers, 2009.

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Book chapters on the topic "Nonlinear wave theories"

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Manasseh, Richard. "Introduction to some nonlinear wave theories." In Fluid Waves. CRC Press, 2021. http://dx.doi.org/10.1201/9780429295263-7.

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Sugimoto, Nobumasa, and Dai Shimizu. "Linear and Nonlinear Theories for Thermoacoustic Waves in a Gas Filled Tube Subject to a Temperature Gradient." In Applied Wave Mathematics II. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-29951-4_9.

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Castagnino, Mario, Jorge Guerón, and Adolfo Ordoñez. "A theorem on wave packets." In Nonlinear Phenomena and Complex Systems. Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-1-4020-2149-7_9.

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Racke, Reinhard. "Global solutions to wave equations — existence theorems." In Lectures on Nonlinear Evolution Equations. Vieweg+Teubner Verlag, 1992. http://dx.doi.org/10.1007/978-3-663-10629-6_2.

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Racke, Reinhard. "Global solutions to wave equations — existence theorems." In Lectures on Nonlinear Evolution Equations. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-21873-1_2.

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Kenig, Carlos. "Universal Profiles and Rigidity Theorems for the Energy Critical Wave Equation." In Nonlinear Partial Differential Equations. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25361-4_8.

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Raynovskyy, Ihor, and Alexander Timokha. "Nonlinear modal theories of nonparametric resonant waves in an upright circular container." In Sloshing in Upright Circular Containers. CRC Press, 2020. http://dx.doi.org/10.1201/9780429356711-4.

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Kazakov, A. L., P. A. Kuznetsov, and A. A. Lempert. "On a Heat Wave for the Nonlinear Heat Equation: An Existence Theorem and Exact Solution." In Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-38870-6_29.

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Selmi, Ridha, and Rim Nasfi. "Exponential Mixing and Ergodic Theorems for a Damped Nonlinear Wave Equation with Space-Time Localised Noise." In Trends in Mathematics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-04459-6_21.

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"Nonlinear Wave Theories." In Advanced Series on Ocean Engineering. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774828_0006.

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Conference papers on the topic "Nonlinear wave theories"

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Zhao, Yuxing, Graham Town, and Mark Sceats. "The Third Order Nonlinearity-A Factor Limiting High SH Efficiency In Optical Fibres." In Nonlinear Guided-Wave Phenomena. Optica Publishing Group, 1993. http://dx.doi.org/10.1364/nlgwp.1993.md.3.

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Second harmonic generation (SHG) in optical glass fibres [1] is an unexpected but nevertheless potentially useful nonlinear phenomenon. Optical fibres offer several advantages in SHG over other devices. Firstly the combination of a long interaction length together with the high intensity possible in a small core permits the relatively small non-linear effects in glasses to be effectively utilised. Furthermore, the self-writing process of SHG in optical fibres may provide an automatic phase matching [2] which is vital in any efficient wave-mixing process. However since observation of efficient
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Afanasjev, V. V. "Interpretation of the effect of reduction of soliton interaction by bandwidth limited amplification." In Nonlinear Guided-Wave Phenomena. Optica Publishing Group, 1993. http://dx.doi.org/10.1364/nlgwp.1993.tub.3.

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A lot of possible applications of solitons for all-optical logic and high-bit rate transmission lines makes the problem of soliton interaction a very important aspect of the study of soliton propagation and amplification in optical fibers. In particular, soliton-soliton interaction limits bit rate of soliton communication systems and therefore reduction of soliton interaction is a very promising proposal. It was discussed recently by different authors that the interaction strength might be substantially reduced or fully suppressed by the bandwidth-limited gain [1-5]. At the same time, the band
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Vitrant, G., R. Reinisch, J. Cl Paumier, G. Assanto, and G. I. Stegeman. "Nonlinear Prism Coupler with Diffusion." In Nonlinear Guided-Wave Phenomena. Optica Publishing Group, 1989. http://dx.doi.org/10.1364/nlgwp.1989.fb3.

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The salient question which arises when light is coupled via a grating or a prism into a waveguide exhibiting an intensity-dependent refractive index is whether switching occurs with or without bistability under appropriate detuning conditions. There are two prevailing theories. In the first1, a plane wave input is assumed leading to a uniform optically induced index change in the coupling region. In the second2, a finite width incident beam is assumed and the growth of the guided field under the coupler leads to an index change proportional to the local guided wave intensity. The first approac
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Yim, Solomon C., Alfred R. Osborne, and Ali Mohtat. "Nonlinear Ocean Wave Models and Laboratory Simulation of High Seastates and Rogue Waves." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-62706.

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With the increasing demand for marine structures, including ships and wave energy devices, to operate in energetic, high seastates, the need for modeling and simulation of nonlinear ocean wave fields in large-scale wave basins is becoming essential. In response to this demand, a number of large-scale wave basins have been placed into operation over the years and larger and more sophisticated new ones are under planning and construction. In this article, the current state of practice and technical issues in modeling and simulation of high seastate ocean waves are summarized. A novel methodology
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Hua, Cun-cai. "On the Solitary Wave and Periodic Wave Solutions of the Nonlinear Drift-Wave Equation Arising from Magnetized Plasmas." In 2011 Fourth International Workshop on Chaos-Fractals Theories and Applications (IWCFTA). IEEE, 2011. http://dx.doi.org/10.1109/iwcfta.2011.47.

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Hardy, Thomas A., and Nicholas C. Kraus. "Coupling Stokes and Cnoidal Wave Theories in a Nonlinear Refraction Model." In 21st International Conference on Coastal Engineering. American Society of Civil Engineers, 1989. http://dx.doi.org/10.1061/9780872626874.043.

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Gruneisen, Mark T., Alexander L. Gaeta, and Robert W. Boyd. "Theory of pump-wave propagation and its effect on degenerate four-wave mixing." In OSA Annual Meeting. Optica Publishing Group, 1985. http://dx.doi.org/10.1364/oam.1985.thj3.

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We have derived an analytic expression for the intensity distribution of two counterpropagating waves of arbitrary input intensity in a saturable absorber. We use this distribution to extend the theory of degenerate four-wave mixing to include the effects of pump wave absorption. In particular, the spatial variation of the nonlinear absorption and coupling constants that appear in the coupled-amplitude equations for the probe and the signal (i.e., conjugate) waves are determined. These coupled-amplitude equations are solved numerically in a noniterative manner, leading to a prediction for the
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Nabelek, Patrik, and Solomon C. Yim. "Riemann-Hilbert Formulation and Solution of Nonlinear Shallow-Water Wave Equations: Nonlocal Dbar Problem as a Unified Approach to Computing Exact Solutions in the Time Domain." In ASME 2023 42nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/omae2023-108051.

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Abstract Linear wave theories and stochastic linear wave spectra are foundational to ocean and coastal engineering. However, there are some important limitations with linear wave theories, and some of which were originally observed experimentally more than a century ago by John Scott Russell. Nonlinearities will cause the linear wave spectra to evolve in time and space as waves move across a basin, or as waves evolve in the ocean and coastal waters, and in coastal channels. Using a nonlinear wave theory can therefore allow researchers and engineers to better capture the dynamic nature of the o
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Yan, Fang, and Haihong Liu. "Exact Travelling Wave Solutions and the Bifurcation for Nonlinear Evolution Modified ZK Equation." In 2010 International Workshop on Chaos-Fractals Theories and Applications (IWCFTA). IEEE, 2010. http://dx.doi.org/10.1109/iwcfta.2010.83.

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Schlo̸er, Signe, Henrik Bredmose, and Harry B. Bingham. "Irregular Wave Forces on Monopile Foundations: Effect of Full Nonlinearity and Bed Slope." In ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2011. http://dx.doi.org/10.1115/omae2011-49709.

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Forces on a monopile from a nonlinear irregular unidirectional wave model are investigated. Two seabed profiles of different slopes are considered. Morison’s equation is used to investigate the forcing from fully nonlinear irregular waves and to compare the results with those obtained from linear wave theory and with stream function wave theory. The latter of these theories is only valid on a flat bed. The three predictions of wave forces are compared and the influence of the bed slope is investigated. Force-profiles of two selected waves from the irregular wave train are further compared with
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