\(N\)-soliton solutions for the integrable bidirectional sixth-order Sawada-Kotera equation

DOI10.1016/j.amc.2010.03.072zbMath1192.35156OpenAlexW2077486572MaRDI QIDQ983979

Abdul-Majid Wazwaz

Publication date: 13 July 2010

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

Full work available at URL: https://doi.org/10.1016/j.amc.2010.03.072

zbMATH Keywords

Cole-Hopf transformationresonanceHirota bilinear methodSawada-Kotera equationmultiple soliton solutionssingular soliton solutions

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Geometric theory, characteristics, transformations in context of PDEs (35A30) Soliton solutions (35C08)

Related Items

Single soliton solutions of the coupled nonlinear Klein-Gordon equations with power law nonlinearity ⋮ A new method of generating the lump molecules and localized interaction solutions to the \((2+1)\)-dimensional SK equation ⋮ Lie symmetry analysis and different types of solutions to a generalized bidirectional sixth-order Sawada-Kotera equation ⋮ Bidirectional solitons and interaction solutions for a new integrable fifth-order nonlinear equation with temporal and spatial dispersion ⋮ Multiple soliton solutions and fusion interaction phenomena for the \((2 + 1)\)-dimensional modified dispersive water-wave system ⋮ A hierarchy of new nonlinear evolution equations and generalized bi-Hamiltonian structures ⋮ The soliton solutions and long-time asymptotic analysis for a general coupled KdV equation ⋮ A new set and new relations of multiple soliton solutions of (2 + 1)-dimensional Sawada-Kotera equation ⋮ New (3+1)-dimensional nonlinear equations with KdV equation constituting its main part: multiple soliton solutions ⋮ \(N\)-soliton and quasi-periodic solutions of the KdV6 equations

Uses Software

• MACSYMA
• HIROTA.MAX

Cites Work

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• KdV6: an integrable system
• Symbolic methods to construct exact solutions of nonlinear partial differential equations
• The Hirota's direct method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera-Ito seventh-order equation
• Multiple-front solutions for the Burgers-Kadomtsev-Petviashvili equation
• Multiple-soliton solutions for the Lax-Kadomtsev-Petviashvili (Lax-KP) equation
• The Hirota's direct method for multiple-soliton solutions for three model equations of shallow water waves
• Multiple-soliton solutions of two extended model equations for shallow water waves
• Multiple-soliton solutions for the Boussinesq equation
• The Cole-Hopf transformation and multiple soliton solutions for the integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota equation
• The tanh method: A tool for solving certain classes of nonlinear evolution and wave equations.
• Integrable KdV systems: Recursion operators of degree four
• New solitons and kink solutions for the Gardner equation
• Multiple-soliton solutions for the KP equation by Hirota's bilinear method and by the tanh-coth method
• Multiple-front solutions for the Burgers equation and the coupled Burgers equations
• A note on ``The integrable KdV6 equation: Multiple soliton solutions and multiple singular soliton solutions
• The integrable KdV6 equations: Multiple soliton solutions and multiple singular soliton solutions
• On bidirectional fifth-order nonlinear evolution equations, Lax pairs, and directionally dependent solitary waves
• N-Soliton Solutions of Model Equations for Shallow Water Waves
• An Extension of Nonlinear Evolution Equations of the K-dV (mK-dV) Type to Higher Orders
• Solitary wave solutions of nonlinear wave equations
• Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
• A New Form of Backlund Transformations and Its Relation to the Inverse Scattering Problem
• A search for bilinear equations passing Hirota’s three-soliton condition. I. KdV-type bilinear equations
• A search for bilinear equations passing Hirota’s three-soliton condition. II. mKdV-type bilinear equations
• The tanh method: II. Perturbation technique for conservative systems
• The tanh method: I. Exact solutions of nonlinear evolution and wave equations
• A new integrable generalization of the Korteweg–de Vries equation