Explicit travelling wave solutions of variants of the \(K(n,n)\) and the \(ZK(n,n)\) equations with compact and noncompact structures

DOI10.1016/j.amc.2005.02.050zbMath1089.65113OpenAlexW2042667943MaRDI QIDQ2489167

Abdul-Majid Wazwaz

Publication date: 16 May 2006

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

Full work available at URL: https://doi.org/10.1016/j.amc.2005.02.050

zbMATH Keywords

Korteweg-de Vries equationtanh method\(K(n,n)\) equationCompactonsSine-cosine methodKadomtsov-Petviashivilli equationZackharov-Kuznetsov equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (14)

Semi-analytical and Numerical Study on Equatorial Rossby Solitary Waves Under Non-traditional Approximation ⋮ The bifurcation and peakon for \(K(2, 2)\) equation with osmosis dispersion ⋮ Smooth and non-smooth traveling wave solutions of a class of nonlinear dispersive equation ⋮ Compacton and solitary pattern solutions for nonlinear dispersive KdV-type equations involving Jumarie's fractional derivative ⋮ Dynamical behaviors of traveling wave solutions of a generalized \(K(N,2n, -N)\) equations ⋮ Jacobi elliptic function solutions of the generalized Zakharov-Kuznetsov equation with nonlinear dispersion and \(t\)-dependent coefficients ⋮ Construction of solitary solutions for nonlinear dispersive equations by variational iteration method ⋮ Different physical structures of solutions for two related Zakharov-Kuznetsov equations ⋮ 1-soliton solution of the generalized Zakharov-Kuznetsov equation with nonlinear dispersion and time-dependent coefficients ⋮ The new exact solitary and multi-soliton solutions for the \((2+1)\)-dimensional Zakharov-Kuznetsov equation ⋮ Construction of solitary wave solutions for variants of theK(n, n) equation ⋮ Dynamical behavior of loop solutions for the \(K(2, 2)\) equation ⋮ Bifurcations of travelling wave solutions for the \(K(n,-n,2n)\) equations ⋮ A repository of equations with cosine/sine compactons

Uses Software

• MACSYMA
• ATFM

Cites Work

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• General solutions with solitary patterns for the defocusing branch of the nonlinear dispersive \(K(n,n)\) equations in higher dimensional spaces
• An analytic study of compactons structures in a class of nonlinear dispersive equations
• Variants of the generalized fifth-order KdV equation with compact and noncompact structures
• The tanh method for traveling wave solutions of nonlinear equations
• The Modified Korteweg-de Vries Equation
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• Solitary wave solutions of nonlinear wave equations
• The tanh method: II. Perturbation technique for conservative systems
• Compactons: Solitons with finite wavelength
• Model equations for long waves in nonlinear dispersive systems
• Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA
• A study of nonlinear dispersive equations with solitary-wave solutions having compact support
• New solitary-wave special solutions with compact support for the nonlinear dispersive \(K(m,n)\) equations

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