Soliton perturbation theory for nonlinear wave equations

DOI10.1016/J.AMC.2010.03.056zbMath1192.35150OpenAlexW2033248487MaRDI QIDQ979323

Laila Girgis, Anjan Biswas

Publication date: 25 June 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.03.056

zbMATH Keywords

perturbationfixed pointsolitons

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Perturbations in context of PDEs (35B20)

Related Items (10)

Soliton dynamics of a high-density Bose-Einstein condensate subject to a time varying anharmonic trap ⋮ Runge-Kutta integration of the equal width wave equation using the method of lines ⋮ Comparative analysis of bore propagation over long distances using conventional linear and KdV-based nonlinear Fourier transform ⋮ Removing trailing tails and delays induced by artificial dissipation in Padé numerical schemes for stable compacton collisions ⋮ Dissipative perturbations for the \(K(n, n)\) Rosenau-Hyman equation ⋮ Bäcklund transformation, superposition formulae and \(N\)-soliton solutions for the perturbed Korteweg-de Vries equation ⋮ A study of shallow water waves with Gardner's equation ⋮ Solving unsteady Korteweg–de Vries equation and its two alternatives ⋮ Applications of He's principles to partial differential equations ⋮ A study of solitary waves by He's semi-inverse variational principle

Cites Work

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• Soliton solutions for \((2+1)\)-dimensional and \((3+1)\)-dimensional \(K(m, n)\) equations
• Bright and dark soliton solutions for a \(K(m,n)\) equation with \(t\)-dependent coefficients
• Adiabatic parameter dynamics of perturbed solitary waves
• 1-soliton solution of the \(K(m,n)\) equation with generalized evolution
• 1-soliton solution of Benjamin-Bona-Mahoney equation with dual-power law nonlinearity
• Travelling wave solutions for a class of the generalized Benjamin-Bona-Mahoney equations
• New solitons and kink solutions for the Gardner equation
• New sets of solitary wave solutions to the KdV, mKdV, and the generalized KdV equations
• Higher-order KdV-type equations and their stability

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