Negative-order KdV and negative-order KP equations: multiple soliton solutions

DOI10.1007/s40010-017-0349-6zbMath1381.35013OpenAlexW2590362739MaRDI QIDQ1700282

Abdul-Majid Wazwaz

Publication date: 5 March 2018

Published in: Proceedings of the National Academy of Sciences, India. Section A. Physical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40010-017-0349-6

zbMATH Keywords

KdV equationKP equationmultiple soliton solutionsinverse recursion operator

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton solutions (35C08)

Related Items (11)

Breather solutions of a negative order modified Korteweg-de Vries equation and its nonlinear stability ⋮ Residual symmetries and soliton-cnoidal wave interaction solutions for the negative-order Korteweg-de Vries equation ⋮ Two new integrable modified KdV equations, of third-and fifth-order, with variable coefficients: multiple real and multiple complex soliton solutions ⋮ Negative order mKdV equation and \(N\)-solitons ⋮ Repeated application of the recursion operator for a new hierarchy of negative-order integrable KdV equations ⋮ Wave solutions to an integrable negative order KdV equation ⋮ Various exact analytical solutions of a variable-coefficient Kadomtsev-Petviashvili equation ⋮ The integrable Vakhnenko-Parkes (VP) and the modified Vakhnenko-parkes (MVP) equations: multiple real and complex soliton solutions ⋮ Multiple complex soliton solutions for integrable negative-order KdV and integrable negative-order modified KdV equations ⋮ Nonlocal symmetry and Bäcklund transformation of a negative-order Korteweg-de Vries equation ⋮ Two new integrable Kadomtsev–Petviashvili equations with time-dependent coefficients: multiple real and complex soliton solutions

Uses Software

• PDERecursionOperator

Cites Work

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• Burgers hierarchy: multiple kink solutions and multiple singular kink solutions
• Multiple soliton solutions for a \((2 + 1)\)-dimensional integrable KdV6 equation
• Exact solutions to the double sinh-Gordon equation by the tanh method and a variable separated ODE method
• Soliton scattering with amplitude changes of a negative order AKNS equation
• Partial differential equations and solitary waves theory
• Variants of a (3+1)-dimensional generalized BKP equation: multiple-front waves solutions
• Integrable systems and their recursion operators.
• Exact solutions and conservation laws of Zakharov-Kuznetsov modified equal width equation with power law nonlinearity
• The tanh and the sine-cosine methods for the complex modified KdV and the generalized KdV equations
• The integrable KdV6 equations: Multiple soliton solutions and multiple singular soliton solutions
• Negative powers of Olver recursion operators
• A symbolic algorithm for computing recursion operators of nonlinear partial differential equations
• Symmetries and Integrability
• Evolution equations possessing infinitely many symmetries

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