Solitary wave solutions of the MKdV\(^-\) equation

DOI10.1016/0045-7825(94)00755-CzbMath0945.65520OpenAlexW2124691356MaRDI QIDQ1578655

L. R. T. Gardner, G. A. Gardner, Turabi Geyikli

Publication date: 4 September 2000

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0045-7825(94)00755-c

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (16)

The large-time asymptotic solution of the mKdV equation ⋮ Solitary wave solutions and kink wave solutions for a generalized KdV-mKdV equation ⋮ A meshless method for solving mKdV equation ⋮ An initial-value problem for the defocusing modified Korteweg-de Vries equation ⋮ A new high-order energy-preserving scheme for the modified Korteweg-de Vries equation ⋮ Discrete conservation laws and the convergence of long time simulations of the mKdV equation ⋮ Existence of exotic waves for the nonlinear dispersive mKdV equation ⋮ Modelling solitary waves of a fifth-order non-linear wave equation ⋮ The β Fermi-Pasta-Ulam-Tsingou recurrence problem ⋮ New traveling wave solutions and interesting bifurcation phenomena of generalized KdV-mKdV-like equation ⋮ SOME COMMON EXPRESSIONS AND NEW BIFURCATION PHENOMENA FOR NONLINEAR WAVES IN A GENERALIZED mKdV EQUATION ⋮ An application for a modified KdV equation by the decomposition method and finite element method ⋮ Comparison of the solutions obtained by B-spline FEM and ADM of KdV equation ⋮ Linearly implicit and second-order energy-preserving schemes for the modified Korteweg-de Vries equation ⋮ Bifurcations of Nonlinear Waves in the Generalized KdV–mKdV-Like Equation ⋮ Numerical solution of a coupled modified Korteweg–de Vries equation by the Galerkin method using quadratic B-splines

Cites Work

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• Analytical and numerical aspects of certain nonlinear evolution equations. IV: Numerical, modified Korteweg-de Vries equation
• Simulations of solitons using quadratic spline finite elements
• The boundary forced MKdV equation
• Subdomain finite element method with quartic B-splines for the modified equal width wave equation
• Formation of shocklike modified Korteweg–de Vries solitons: Application to double layers
• A numerical and theoretical study of certain nonlinear wave phenomena
• Weak Nonlinear Dispersive Waves: A Discussion Centered Around the Korteweg–De Vries Equation

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