Numerical analysis of soliton solutions of the modified Korteweg-de Vries-sine-Gordon equation

DOI10.1134/S0965542515030136zbMath1321.65156MaRDI QIDQ2354461

S. P. Popov

Publication date: 13 July 2015

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Runge-Kutta methodsolitonmultisoliton interactionmultisoliton solutionsantikinkbreatherkinkgraphical examplesquasi-spectral Fourier methodmodified Korteweg-de Vries-sine-Gordon equationnonlinear oscillatory waveswobbler

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Soliton equations (35Q51) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (8)

New compacton solutions of an extended Rosenau-Pikovsky equation ⋮ Superconvergence of the local discontinuous Galerkin method for the sine-Gordon equation in one space dimension ⋮ Optimal energy-conserving local discontinuous Galerkin method for the one-dimensional sine-Gordon equation ⋮ Compactons and Riemann waves of an extended modified Korteweg-de Vries equation with nonlinear dispersion ⋮ Soliton solutions of a generalization of the coupled Volterra system ⋮ Complex simplified Hirota's forms and Lie symmetry analysis for multiple real and complex soliton solutions of the modified KdV-sine-Gordon equation ⋮ Compacton solutions of the Korteweg-de Vries equation with constrained nonlinear dispersion ⋮ Numerical evaluations of periodic wave solutions, integrable time discretization and their applications to the mKdV–sine-Gordon equation

Cites Work

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• Conservation laws for some nonlinear evolution equations which describe pseudo-spherical surfaces
• Exponential time differencing for stiff systems
• The Bäcklund transformations, exact solutions, and conservation laws for the compound modified Korteweg-de Vries-Sine-Gordon equations which describe pseudospherical surfaces
• Influence of dislocations on kink solutions of the double sine-Gordon equation
• Structure and properties of four-kink multisolitons of the sine-Gordon equation
• Application of the quasi-spectral fourier method to soliton equations
• On the nonlinear stability of mKdV breathers
• The sine-Gordon wobble
• Few-optical-cycle dissipative solitons
• The Novel Multi-Soliton Solutions of the MKdV–Sine Gordon Equations
• Solitary wave solutions of the short pulse equation
• Perturbed soliton solutions of the sine-Gordon equation

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