New exact solutions for the KdV equation with higher order nonlinearity by using the variational method

DOI10.1016/j.camwa.2011.09.023zbMath1236.35156OpenAlexW2095184008MaRDI QIDQ2429018

Aly R. Seadawy

Publication date: 22 April 2012

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2011.09.023

zbMATH Keywords

exact solutionsKdV equationcalculus of variationspartial differential equationsLagrangian and Hamiltonian mechanics

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Variational methods applied to PDEs (35A15) Solutions to PDEs in closed form (35C05)

Related Items (37)

Nonlinear wave solutions of the three-dimensional Zakharov-Kuznetsov-Burgers equation in dusty plasma ⋮ Stability analysis solutions for nonlinear three-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation in a magnetized electron-positron plasma ⋮ Multi-symplectic quasi-interpolation method for the KdV equation ⋮ Propagation of traveling wave solutions to the Vakhnenko-Parkes dynamical equation via modified mathematical methods ⋮ Solitary wave solutions of few nonlinear evolution equations ⋮ Stability analysis for Zakharov-Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma ⋮ Stability analysis of solitary wave solutions for the fourth-order nonlinear Boussinesq water wave equation ⋮ Three-Dimensional Weakly Nonlinear Shallow Water Waves Regime and its Traveling Wave Solutions ⋮ Structure of optical solitons of resonant Schrödinger equation with quadratic cubic nonlinearity and modulation instability analysis ⋮ Dispersive wave propagation of the nonlinear Sasa-Satsuma dynamical system with computational and analytical soliton solutions ⋮ Periodic-wave and semirational solutions for the \((2 + 1)\)-dimensional Davey-Stewartson equations on the surface water waves of finite depth ⋮ Stability analysis and applications of traveling wave solutions of three-dimensional nonlinear modified Zakharov–Kuznetsov equation in a magnetized plasma ⋮ Computational analysis of the third order dispersive fractional <scp>PDE</scp> under exponential‐decay and <scp>Mittag‐Leffler</scp> type kernels ⋮ Single soliton and double soliton solutions of the quadratic‐nonlinear Korteweg‐de Vries equation for small and long‐times ⋮ Stability analysis of solutions for the sixth-order nonlinear Boussinesq water wave equations in two-dimensions and its applications ⋮ Travelling wave solutions of Drinfel'd-Sokolov-Wilson, Whitham-Broer-Kaup and \((2+1)\)-dimensional Broer-Kaup-Kupershmit equations and their applications ⋮ Dynamical behaviors of different wave structures to the Korteweg-de Vries equation with the Hirota bilinear technique ⋮ Solitary wave solutions of \((3+1)\)-dimensional extended Zakharov-Kuznetsov equation by Lie symmetry approach ⋮ Construction and solitary wave solutions of two-mode higher-order Boussinesq-Burger system ⋮ Ion acoustic solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili-Burgers equation in quantum plasma ⋮ Dispersive analytical soliton solutions of some nonlinear waves dynamical models via modified mathematical methods ⋮ Traveling wave solutions of the Benjamin-Bona-Mahony water wave equations ⋮ Studies of wave interaction of high-order Korteweg-de Vries equation by means of the homotopy strategy and neural network prediction ⋮ Kinky breathers, multi-peak and multi-wave soliton solutions for the nonlinear propagation of Kundu–Eckhaus dynamical model ⋮ Optical soliton and elliptic functions solutions of Sasa-Satsuma dynamical equation and its applications ⋮ Study on numerical solution of dispersive water wave phenomena by using a reliable modification of variational iteration algorithm ⋮ Rogue waves, bright-dark solitons and traveling wave solutions of the \((3+1)\)-dimensional generalized Kadomtsev-Petviashvili equation ⋮ Fractional solitary wave solutions of the nonlinear higher-order extended KdV equation in a stratified shear flow. I ⋮ Three-dimensional nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma ⋮ Closed form solutions of two nonlinear equation via the enhanced (G^′/G)-expansion method ⋮ Modification of quintic B-spline differential quadrature method to nonlinear Korteweg-de Vries equation and numerical experiments ⋮ Numerical simulation for the solitary wave of Zakharov-Kuznetsov equation based on lattice Boltzmann method ⋮ Rogue waves generation and interaction of multipeak rational solitons in the system of equations for the ion sound and Langmuir waves ⋮ Classification of multiply travelling wave solutions for coupled Burgers, combined KdV-modified KdV, and Schrödinger-KdV equations ⋮ Painlevé analysis for various nonlinear Schrödinger dynamical equations ⋮ Soliton solutions for (2+1) and (3+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony model equations and their applications ⋮ Soliton solutions of cubic-quintic nonlinear Schrödinger and variant boussinesq equations by the first integral method

Uses Software

• PDESpecialSolutions
• ATFM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Symbolic methods to construct exact solutions of nonlinear partial differential equations
• Abundant solitons solutions for several forms of the fifth-order KdV equation by using the tanh method
• Soliton perturbation theory for the compound KdV equation
• An automated \(\tanh\)-function method for finding solitary wave solutions to nonlinear evolution equations
• Symbolic computations of conserved densities for systems of nonlinear evolution equations
• Invariant variational principles and conservation laws for some nonlinear partial differential equations with variable coefficients. II
• Lyapunov approach to the soliton stability in highly dispersive systems. II: KdV-type equations
• Exact solutions of some fifth-order nonlinear equations
• Cnoidal wave solutions for a class of fifth-order KdV equations
• Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs
• An Extension of Nonlinear Evolution Equations of the K-dV (mK-dV) Type to Higher Orders
• An investigation of internal solitary waves in a two-fluid system
• A second-order theory for solitary waves in shallow fluids
• Long Non‐Linear Waves in Fluid Flows
• Variational principle for the Zakharov-Shabat equations

This page was built for publication: New exact solutions for the KdV equation with higher order nonlinearity by using the variational method