On the rational solitary wave solutions for the nonlinear Hirota–Satsuma coupled KdV system

DOI10.1080/00036810600604789zbMath1106.35088OpenAlexW1969331723WikidataQ58266491 ScholiaQ58266491MaRDI QIDQ5481702

M. M. El Horbaty, Khaled A. Gepreel, Elsayed M. E. Zayed, Aly Maher Abourabia

Publication date: 10 August 2006

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036810600604789

zbMATH Keywords

symbolic computationrational solitary wave solutions

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Solutions to PDEs in closed form (35C05)

Related Items (9)

Extended proposed algorithm with symbolic computation to construct exact solutions for some nonlinear differential equations ⋮ Solutions and conservation laws of a (3+1)-dimensional Zakharov-Kuznetsov equation ⋮ Applications of the extended rational sine-cosine and sinh-cosh techniques to some nonlinear complex models arising in mathematical physics ⋮ On the exact solutions to some system of complex nonlinear models ⋮ Exact solutions for some non-linear differential equations using complex hyperbolic function methods ⋮ Exact solutions for nonlinear differential difference equations in mathematical physics ⋮ A series of complexiton soliton solutions for non-linear Hirota–Satsuma equations using the generalized multiple Riccati equations rational expansion method ⋮ On using the modified variational iteration method for solving the nonlinear coupled equations in the mathematical physics ⋮ Some applications of the \((\frac{G'}{G})\)-expansion method to non-linear partial differential equations

Uses Software

• Maple
• Mathematica

Cites Work

• A series of new exact solutions for a complex coupled KdV system
• The sec\(_q\)-tanh\(_q\)-method and its applications
• New transformations and new approach to find exact solutions to nonlinear equations
• On the solitary wave solutions for nonlinear Hirota-Satsuma coupled KdV equations
• Group analysis and modified extended tanh-function to find the invariant solutions and soliton solutions for nonlinear Euler equations
• New travelling wave solutions of the generalized coupled Hirota-Satsuma KdV system
• A complex tanh-function method applied to nonlinear equations of Schrödinger type
• A generalized Hirota-Satsuma coupled Korteweg-de Vries equation and Miura transformations
• Explicit exact solutions for new general two-dimensional KdV-type and two-dimensional KdV Burgers-type equations with nonlinear terms of any order
• On the solitary wave solutions for nonlinear Euler equations
• Soliton solutions for a generalized Hirota-Satsuma coupled KdV equation and a coupled MKdV equation
• Double periodic solutions with Jacobi elliptic functions for two generalized Hirota-Satsuma coupled KdV systems
• New exact solutions for a class of nonlinear coupled differential equations

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