Relevant bibliographies by topics / Ginzburg-Landau equation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
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Academic literature on the topic 'Ginzburg-Landau equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Ginzburg-Landau equation"

1

CHIRON, DAVID. "BOUNDARY PROBLEMS FOR THE GINZBURG–LANDAU EQUATION." Communications in Contemporary Mathematics 07, no. 05 (2005): 597–648. http://dx.doi.org/10.1142/s0219199705001908.

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We provide a study at the boundary for a class of equations including the Ginzburg–Landau equation as well as the equation of travelling waves for the Gross–Pitaevskii model. We prove Clearing-Out results and an orthogonal anchoring condition of the vortex on the boundary for the Ginzburg–Landau equation with magnetic field.
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Adomian, G., and R. E. Meyers. "The Ginzburg-Landau equation." Computers & Mathematics with Applications 29, no. 3 (1995): 3–4. http://dx.doi.org/10.1016/0898-1221(94)00222-7.

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Gao, Hongjun, and Keng-Huat Kwek. "Global existence for the generalised 2D Ginzburg-Landau equation." ANZIAM Journal 44, no. 3 (2003): 381–92. http://dx.doi.org/10.1017/s1446181100008099.

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AbstractGinzburg-Landau type complex partial differential equations are simplified mathematical models for various pattern formation systems in mechanics, physics and chemistry. Most work so far has concentrated on Ginzburg-Landau type equations with one spatial variable (1D). In this paper, the authors study a complex generalised Ginzburg-Landau equation with two spatial variables (2D) and fifth-order and cubic terms containing derivatives. Based on detail analysis, sufficient conditions for the existence and uniqueness of global solutions are obtained.
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Li, Xiao-Yu, Yu-Lan Wang, and Zhi-Yuan Li. "Numerical simulation for the fractional-in-space Ginzburg-Landau equation using Fourier spectral method." AIMS Mathematics 8, no. 1 (2022): 2407–18. http://dx.doi.org/10.3934/math.2023124.

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<abstract><p>This paper uses the Fourier spectral method to study the propagation and interaction behavior of the fractional-in-space Ginzburg-Landau equation in different parameters and different fractional derivatives. Comparisons are made between the numerical and the exact solution, and it is found that the Fourier spectral method is a satisfactory and efficient algorithm for capturing the propagation of the fractional-in-space Ginzburg-Landau equation. Experimental findings indicate that the proposed method is easy to implement, effective and convenient in the long-time simula
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Ipsen, M., F. Hynne, and P. G. Sørensen. "Amplitude Equations and Chemical Reaction–Diffusion Systems." International Journal of Bifurcation and Chaos 07, no. 07 (1997): 1539–54. http://dx.doi.org/10.1142/s0218127497001217.

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The paper discusses the use of amplitude equations to describe the spatio-temporal dynamics of a chemical reaction–diffusion system based on an Oregonator model of the Belousov–Zhabotinsky reaction. Sufficiently close to a supercritical Hopf bifurcation the reaction–diffusion equation can be approximated by a complex Ginzburg–Landau equation with parameters determined by the original equation at the point of operation considered. We illustrate the validity of this reduction by comparing numerical spiral wave solutions to the Oregonator reaction–diffusion equation with the corresponding solutio
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Ali, Khalid K., M. Maneea, and Mohamed S. Mohamed. "Solving Nonlinear Fractional Models in Superconductivity Using the q-Homotopy Analysis Transform Method." Journal of Mathematics 2023 (August 11, 2023): 1–23. http://dx.doi.org/10.1155/2023/6647375.

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The Ginzburg–Landau (GL) equation and the Ginzburg–Landau couple system are important models in the study of superconductivity and superfluidity. This study describes the q-homotopy analysis transform method (q-HATM) as a powerful technique for solving nonlinear problems, which has been successfully used with a set of mathematical models in physics, engineering, and biology. We apply the q-HATM to solve the Ginzburg–Landau equation and the Ginzburg–Landau coupled system and derive analytical solutions in terms of the q-series. Also, we investigate the convergence and accuracy of the obtained s
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Huang, Chunyan. "On the Analyticity for the Generalized Quadratic Derivative Complex Ginzburg-Landau Equation." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/607028.

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We study the analytic property of the (generalized) quadratic derivative Ginzburg-Landau equation(1/2⩽α⩽1)in any spatial dimensionn⩾1with rough initial data. For1/2<α⩽1, we prove the analyticity of local solutions to the (generalized) quadratic derivative Ginzburg-Landau equation with large rough initial data in modulation spacesMp,11-2α(1⩽p⩽∞). Forα=1/2, we obtain the analytic regularity of global solutions to the fractional quadratic derivative Ginzburg-Landau equation with small initial data inB˙∞,10(ℝn)∩M∞,10(ℝn). The strategy is to develop uniform and dyadic exponential decay estimates
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Barybin, Anatoly A. "Nonstationary Superconductivity: Quantum Dissipation and Time-Dependent Ginzburg-Landau Equation." Advances in Condensed Matter Physics 2011 (2011): 1–10. http://dx.doi.org/10.1155/2011/425328.

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Transport equations of the macroscopic superfluid dynamics are revised on the basis of a combination of the conventional (stationary) Ginzburg-Landau equation and Schrödinger's equation for the macroscopic wave function (often called the order parameter) by using the well-known Madelung-Feynman approach to representation of the quantum-mechanical equations in hydrodynamic form. Such an approach has given (a) three different contributions to the resulting chemical potential for the superfluid component, (b) a general hydrodynamic equation of superfluid motion, (c) the continuity equation for su
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Salem, Ahmed, and Rania Al-Maalwi. "Fractional Evolution Equation with Nonlocal Multi-Point Condition: Application to Fractional Ginzburg–Landau Equation." Axioms 14, no. 3 (2025): 205. https://doi.org/10.3390/axioms14030205.

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This paper is devoted to studying the existence and uniqueness of mild solutions for semilinear fractional evolution equations with the Hilfer–Katugampola fractional derivative and under the nonlocal multi-point condition. The analysis is based on analytic semigroup theory, the Krasnoselskii fixed-point theorem, and the Banach fixed-point theorem. An application to a time-fractional real Ginzburg–Landau equation is also given to illustrate the applicability of our results. Furthermore, we determine some conditions to make the control (Bifurcation) parameter in the Ginzburg–Landau equation suff
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Secer, Aydin, and Yasemin Bakir. "Chebyshev wavelet collocation method for Ginzburg-Landau equation." Thermal Science 23, Suppl. 1 (2019): 57–65. http://dx.doi.org/10.2298/tsci180920330s.

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The main aim of this paper is to investigate the efficient Chebyshev wavelet collocation method for Ginzburg-Landau equation. The basic idea of this method is to have the approximation of Chebyshev wavelet series of a non-linear PDE. We demonstrate how to use the method for the numerical solution of the Ginzburg-Landau equation with initial and boundary conditions. For this purpose, we have obtained operational matrix for Chebyshev wavelets. By applying this technique in Ginzburg-Landau equation, the PDE is converted into an algebraic system of non-linear equations and this system has been sol
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Dissertations / Theses on the topic "Ginzburg-Landau equation"

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Liu, Weigang. "A General Study of the Complex Ginzburg-Landau Equation." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/90886.

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In this dissertation, I study a nonlinear partial differential equation, the complex Ginzburg-Landau (CGL) equation. I first employed the perturbative field-theoretic renormalization group method to investigate the critical dynamics near the continuous non-equilibrium transition limit in this equation with additive noise. Due to the fact that time translation invariance is broken following a critical quench from a random initial configuration, an independent ``initial-slip'' exponent emerges to describe the crossover temporal window between microscopic time scales and the asymptotic long-time
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Braun, Robert, and Fred Feudel. "Supertransient chaos in the two-dimensional complex Ginzburg-Landau equation." Universität Potsdam, 1996. http://opus.kobv.de/ubp/volltexte/2007/1409/.

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We have shown that the two-dimensional complex Ginzburg-Landau equation exhibits supertransient chaos in a certain parameter range. Using numerical methods this behavior is found near the transition line separating frozen spiral solutions from turbulence. Supertransient chaos seems to be a common phenomenon in extended spatiotemporal systems. These supertransients are characterized by an average transient lifetime which depends exponentially on the size of the system and are due to an underlying nonattracting chaotic set.
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Cruz-Pacheco, Gustavo. "The nonlinear Schroedinger limit of the complex Ginzburg-Landau equation." Diss., The University of Arizona, 1995. http://hdl.handle.net/10150/187238.

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This work consists of a study of the complex Ginzburg-Landau equation (CGL) as a perturbation of the nonlinear Schrodinger equation (NLS) in one dimension under periodic boundary conditions. Using an averaging technique which is similar to a Melnikov method for pde's, necessary conditions are derived for the persistence of NLS solutions under the CGL perturbation. For the traveling wave solutions, these conditions are derived for a general nonlinearity and written explicitly as two equations for the two continuous parameters which determine the NLS traveling wave. It is shown using a Melnikov
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Horsch, Karla 1968. "Attractors for Lyapunov cases of the complex Ginzburg-Landau equation." Diss., The University of Arizona, 1997. http://hdl.handle.net/10150/282419.

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A special case of the complex Ginzburg-Landau (CGL) equation possessing a Lyapunov functional is identified. The global attractor of this Lyapunov CGL (LCGL) is studied in one spatial dimension with periodic boundary conditions. The LCGL may be viewed as a dissipative perturbation of the nonlinear Schrodinger equation (NLS), a completely integrable Hamiltonian system. The o-limit sets of the LCGL are identified as compact, connected unions of subsets of the stationary points of the flow. The stationary points do not depend on the strength of the perturbation, and so neither do the o-limit sets
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Aguareles, Carrero Maria. "Interaction of spiral waves in the general complex Ginzburg-Landau equation." Doctoral thesis, Universitat Politècnica de Catalunya, 2007. http://hdl.handle.net/10803/5854.

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Molts sistemes físics tenen la propietat que la seva dinàmica ve definida per algun tipus de difussió espaial en competició amb un fenòmen de reacció, com per exemple en el cas de dos components químics que reaccionen al mateix temps que es difon l'un en el si de l'altre. La presència d'aquests dos fenòmens, la difusió i la reacció, sovint dóna lloc a patrons no homogenis de gran riquesa. Els models matemàtics que descriuen aquest tipus de comportament són normalment equacions en derivades parcials les solucions de les quals representen aquests patrons. <br/><br/>En aquesta tesi s'analitza l'e
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Banaji, Murad. "Clustering and chaos in globally coupled oscillators." Thesis, Queen Mary, University of London, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249289.

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SNOUSSI, SEIFEDDINE. "Etude du comportement asymptotique des solutions d'une equation de ginzburg-landau generalisee." Paris 11, 1996. http://www.theses.fr/1996PA112060.

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L'objet de cette these est d'etudier les problemes d'existence locale ou globale de solutions d'un systeme couple d'une equation de ginzburg-landau generalisee et une equation de poisson ainsi qu'a l'etude de leur comportement asymptotique. Ce systeme est considere sur un domaine pouvant etre borne ou non-borne et les donnees initiales sont supposees etre de faible regularite. La premiere partie de cette these est consacree a l'etude du comportement asymptotique et qualitative des solutions de ce systeme quand il est considere sur un ouvert borne de la droite reelle ou du plan. On donnera des
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Sauvageot, Myrto. "Modèle de Ginzburg-Landau : solutions radiales et branches de bifurcation." Paris 6, 2002. http://www.theses.fr/2002PA066548.

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Attanasio, Felipe [UNESP]. "Numerical study of the Ginzburg-Landau-Langevin equation: coherent structures and noise perturbation theory." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/92029.

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Made available in DSpace on 2014-06-11T19:25:34Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-02-21Bitstream added on 2014-06-13T19:12:26Z : No. of bitstreams: 1 attanasio_f_me_ift.pdf: 793752 bytes, checksum: 490b63eed4bdd7ec83984c78ac824d6d (MD5)<br>Nesta Dissertação apresentamos um estudo numéerico em uma dimensão espacial da equação de Ginzburg-Landau-Langevin (GLL), com ênfase na aplicabilidade de um método de perturbação estocástico e na mecânica estatística de defeitos topológicos em modelos de campos escalares reais. Revisamos brevemente conceitos de mecânica estatística de
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Attanasio, Felipe. "Numerical study of the Ginzburg-Landau-Langevin equation : coherent structures and noise perturbation theory /." São Paulo, 2013. http://hdl.handle.net/11449/92029.

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Orientador: Gastão Inácio Krein<br>Banca: Raquel Santos Marques de Carvalho<br>Banca: Ricardo D'Elia Matheus<br>Resumo: Nesta Dissertação apresentamos um estudo numéerico em uma dimensão espacial da equação de Ginzburg-Landau-Langevin (GLL), com ênfase na aplicabilidade de um método de perturbação estocástico e na mecânica estatística de defeitos topológicos em modelos de campos escalares reais. Revisamos brevemente conceitos de mecânica estatística de sistemas em equilíbrio e próximos a ele e apresentamos como a equação de GLL pode ser usada em sistemas que exibem transições de fase, na quant
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Books on the topic "Ginzburg-Landau equation"

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Bethuel, Fabrice. Ginzburg-Landau vortices. Birkhäuser, 1994.

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Herbert, Geoffrey M. Stability analysis of the Fisher and Landau-Ginzburg equations. typescript, 1995.

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Duong, Giao Ky, and Nejla Nouaili. Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters. American Mathematical Society, 2023.

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Hélein, Frédéric, Fabrice Bethuel, and Haïm Brezis. Ginzburg-Landau Vortices. Birkhäuser, 2017.

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Helein, Frederic, Haim Brezis, and Fabrice Bethuel. Ginzburg-Landau Vortices. Birkhauser Verlag, 2012.

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Ginzburg-Landau Vortices. World Scientific Publishing Co Pte Ltd, 2005.

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Ginzburg-Landau Vortices. World Scientific Publishing Co Pte Ltd, 2005.

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Horing, Norman J. Morgenstern. Superfluidity and Superconductivity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0013.

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Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (&lt;ψ(x,t)&gt;≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function&lt;ψ&gt;=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i&lt;(ψ˜(1)ψ˜+(1′))+&gt; and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i&lt;(ψ˜+(2)ψ˜+(1′))+&gt; describe the dynamics and elementary excitations of the
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Tang, Q., and K. H. Hoffmann. Ginzburg-Landau Phase Transition Theory and Superconductivity. Birkhäuser Boston, 2012.

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(Editor), Haim Brezis, and Daqian Li (Editor), eds. Ginzburg-landau Vortices (Series in Contemporary Applied Mathematics). World Scientific Publishing Company, 2005.

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Book chapters on the topic "Ginzburg-Landau equation"

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Bethuel, Fabrice, Haïm Brezis, and Frédéric Hélein. "Non-minimizing solutions of the Ginzburg-Landau equation." In Ginzburg-Landau Vortices. Birkhäuser Boston, 1994. http://dx.doi.org/10.1007/978-1-4612-0287-5_10.

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Tarasov, Vasily E. "Fractional Ginzburg-Landau Equation." In Nonlinear Physical Science. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14003-7_9.

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Sirovich, L., and P. K. Newton. "Ginzburg-Landau Equation: Stability and Bifurcations." In Stability of Time Dependent and Spatially Varying Flows. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4612-4724-1_15.

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Tarasov, Vasily E. "Ginzburg-Landau Equation for Fractal Media." In Nonlinear Physical Science. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14003-7_5.

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Ovchinnikov, Yuri, and Israel Sigal. "Ginzburg-Landau equation I. Static vortices." In CRM Proceedings and Lecture Notes. American Mathematical Society, 1997. http://dx.doi.org/10.1090/crmp/012/16.

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Pacard, Frank, and Tristan Rivière. "The Ginzburg-Landau Equation in ℂ." In Linear and Nonlinear Aspects of Vortices. Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1386-4_3.

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Grundland, A. M., J. A. Tuszyński, and P. Winternitz. "Elliptic Function Solutions for Landau-Ginzburg Equation." In Partially Intergrable Evolution Equations in Physics. Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-0591-7_28.

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Akhmediev, Nail, and Adrian Ankiewicz. "Solitons of the Complex Ginzburg—Landau Equation." In Springer Series in Optical Sciences. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-540-44582-1_12.

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Izadi, Mojtaba, Charles R. Koch, and Stevan S. Dubljevic. "Model Predictive Control of Ginzburg-Landau Equation." In Notes on Numerical Fluid Mechanics and Multidisciplinary Design. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-98177-2_5.

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Salerno, Mario, and Fatkhulla Kh Abdullaev. "Discrete Solitons of the Ginzburg-Landau Equation." In Dissipative Optical Solitons. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-97493-0_14.

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Conference papers on the topic "Ginzburg-Landau equation"

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Halder, Kritika, Manoj Mishra, S. Shwetanshumala, Soumendu Jana, and Swapan Konar. "Soliton Collision Dynamics in Multiple Coupled Quantum Well Structure." In Quantum 2.0. Optica Publishing Group, 2024. http://dx.doi.org/10.1364/quantum.2024.qw3a.49.

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The article investigates the impact of the probe and control beam on the propagation and collision dynamics of optical solitons in an MCQW structure incorporating giant higher-order nonlinearities by simulating the complex cubic-quintic Ginzburg-Landau equation.
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Nko’o Nko’o, M. J., A. Djazet, L. M. Mandeng, et al. "Anti-vortex soliton dynamics in systems modelled by a complex cubic-quintic Ginzburg-Landau vector equation." In Frontiers in Optics. Optica Publishing Group, 2024. https://doi.org/10.1364/fio.2024.jd4a.28.

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Using the variational approach, we show that the anti-vortex vector solution is the best which can be managed using the coupling parameters of the system because it is more stable following its rapid soliton transformation.
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Zaslavsky, George M., and Vasily E. Tarasov. "Fractional Generalization of Ginzburg-Landau and Nonlinear Schroedinger Equations." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84266.

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The fractional generalization of the Ginzburg-Landau equation is derived from the variational Euler-Lagrange equation for fractal media. To describe fractal media we use the fractional integrals considered as approximations of integrals on fractals. Some different forms of the fractional Ginzburg-Landau equation or nonlinear Schro¨dinger equation with fractional derivatives are presented. The Agrawal variational principle and its generalization have been applied.
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Brand, Helmut R., Orazio Descalzi, and Jaime Cisternas. "Hole Solutions in the Cubic Complex Ginzburg-Landau Equation versus Holes in the Cubic-Quintic Complex Ginzburg-Landau Equation." In NONEQUILIBRIUM STATISTICAL MECHANICS AND NONLINEAR PHYSICS: XV Conference on Nonequilibrium Statistical Mechanics and Nonlinear Physics. AIP, 2007. http://dx.doi.org/10.1063/1.2746737.

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Hernández Piñeiro, Víctor, Víctor González Tabernero, and Ana María Ferreiro Ferreiro. "Study and Solution of the Ginzburg-Landau Equation for Superconductivity Problems." In VII Congreso XoveTIC: impulsando el talento científico. Servizo de Publicacións. Universidade da Coruña, 2024. https://doi.org/10.17979/spudc.9788497498913.7.

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This work focuses on the study and numerical solution of the Ginzburg-Landau (hereafter referred to as GL) partial differential equation, which models the behavior of superconducting materials. Depending on its parameters, the Ginzburg-Landau model can exhibit chaotic states that are challenging to approximate numerically, requiring the use of high-order numerical schemes. In this work, the resolution of this model was addressed in both the 1D and 2D cases. In both cases, an IMEX-type method based on finite differences was used, which provided good results.
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FURSIKOV, A. V. "ANALYTICITY OF STABLE INVARIANT MANIFOLDS FOR GINZBURG-LANDAU EQUATION." In Applied Analysis and Differential Equations - The International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812708229_0009.

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Saitoh, Kuniyasu, and Hisao Hayakawa. "Time dependent Ginzburg-Landau equation for sheared granular flow." In 28TH INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS 2012. AIP, 2012. http://dx.doi.org/10.1063/1.4769651.

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Guo, Shan, Chao Xu, and Xuemin Tu. "Parameter estimation for Ginzburg-Landau equation via implicit sampling." In 2016 American Control Conference (ACC). IEEE, 2016. http://dx.doi.org/10.1109/acc.2016.7526490.

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Li, Jing, and Zhixiong Zhang. "Complex Ginzburg-Landau equation with boundary control and observation." In 2016 2nd International Conference on Control Science and Systems Engineering (ICCSSE). IEEE, 2016. http://dx.doi.org/10.1109/ccsse.2016.7784365.

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Xiang, Chunhuan, and Honglei Wang. "An approximate method for solving complex Ginzburg-Landau equation." In 2018 8th International Conference on Manufacturing Science and Engineering (ICMSE 2018). Atlantis Press, 2018. http://dx.doi.org/10.2991/icmse-18.2018.111.

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Reports on the topic "Ginzburg-Landau equation"

1

Takac, P. Dynamics on the attractor for the complex Ginzburg-Landau equation. Office of Scientific and Technical Information (OSTI), 1994. http://dx.doi.org/10.2172/10174640.

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Vernov, Sergey Yu. Construction of Elliptic Solutions to the Quintic Complex One-dimensional Ginzburg–Landau Equation. GIQ, 2012. http://dx.doi.org/10.7546/giq-8-2007-322-333.

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Fleckinger-Pelle, J., H. G. Kaper, and P. Takac. Dynamics of the Ginzburg-Landau equations of superconductivity. Office of Scientific and Technical Information (OSTI), 1997. http://dx.doi.org/10.2172/516027.

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Coskun, E., and M. K. Kwong. Parallel solution of the time-dependent Ginzburg-Landau equations and other experiences using BlockComm-Chameleon and PCN on the IBM SP, Intel iPSC/860, and clusters of workstations. Office of Scientific and Technical Information (OSTI), 1995. http://dx.doi.org/10.2172/266722.

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