Construction of new solutions to the fully nonlinear generalized Camassa-Holm equations by an indirect F function method

DOI10.1063/1.2137723zbMath1111.35068OpenAlexW2005429862MaRDI QIDQ3438719

Emmanuel Yomba

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.2137723

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Elliptic functions and integrals (33E05)

Related Items

Constructing of new exact solutions to the GKdV-mKdV equation with any-order nonlinear terms by \((\frac{G'}{G})\)-expansion method ⋮ A note on solitary waves for modified forms of Camassa-Holm and Degasperis-Procesi equations ⋮ The improved \(\exp\left(- \Phi \left(\xi\right)\right)\)-expansion method and new exact solutions of nonlinear evolution equations in mathematical physics ⋮ Jacobi elliptic function solutions of the generalized Zakharov-Kuznetsov equation with nonlinear dispersion and \(t\)-dependent coefficients ⋮ A simple approach for reducing the order of equations with higher order nonlinearity ⋮ Modulational instability and exact solutions for a three-component system of vector nonlinear Schrödinger equations ⋮ The sub-ODE method for finding exact travelling wave solutions of generalized nonlinear Camassa-Holm, and generalized nonlinear Schrödinger equations ⋮ A generalized auxiliary equation method and its application to nonlinear Klein-Gordon and generalized nonlinear Camassa-Holm equations ⋮ Constructing of exact solutions to the KdV and Burgers equations with power-law nonlinearity by the extended \((\frac{G'}{G})\)-expansion method ⋮ Soliton solutions for a negative order non-isospectral AKNS equation

Uses Software

• RATH

Cites Work

• Unnamed Item
• Unnamed Item
• RATH: A Maple package for finding travelling solitary wave solutions to nonlinear evolution equations
• An automated \(\tanh\)-function method for finding solitary wave solutions to nonlinear evolution equations
• Exact solutions for some nonlinear partial differential equations
• Soliton-like and period form solutions for high dimensional nonlinear evolution equations
• Explicit exact solutions for compound KdV-type and compound KdV-Burgers-type equations with nonlinear terms of any order.
• Construction of new soliton-like solutions for the \((2+1)\) dimensional Kadomtsev-Petviashvili equation
• Compactons in a general compressible hyperelastic rod
• Periodic wave solutions to a coupled KdV equations with variable coefficients
• On a further extended tanh method
• New compacton solutions and solitary wave solutions of fully nonlinear generalized Camassa--Holm equations
• Construction of new soliton-like solutions of the (2 + 1) dimensional dispersive long wave equation
• Nonlinear transform and Jacobi elliptic function solutions of nonlinear equations
• On exact solutions of the coupled Klein--Gordon--Schrödinger and the complex coupled KdV equations using mapping method
• Solitary wave solutions for variant Boussinesq equations
• A simple transformation for nonlinear waves.
• The periodic wave solutions and solitary wave solutions for a class of nonlinear partial differential equations
• Rational function representations of wave patterns in higher-dimensional and discrete evolution equations
• New exact solutions of a new \((2+1)\)-dimensional integrable system
• Fractional transformation and new solutions to mKdV equation
• Extended tanh-function method and its applications to nonlinear equations
• Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws
• Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
• An integrable shallow water equation with peaked solitons
• Solitary shock waves and other travelling waves in a general compressible hyperelastic rod
• Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
• New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations