Construction of solitary wave solutions and rational solutions for the KdV equation by Adomian decomposition method
From MaRDI portal
Publication:1600450
DOI10.1016/S0960-0779(00)00188-0zbMath0992.35092OpenAlexW1977556269MaRDI QIDQ1600450
Publication date: 13 June 2002
Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0960-0779(00)00188-0
Adomian decomposition methodexact and approximate solutions for the nonlinear dispersive KdV equation
KdV equations (Korteweg-de Vries equations) (35Q53) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Solutions to PDEs in closed form (35C05) Other special methods applied to PDEs (35A25)
Related Items
Lump, lumpoff, rogue wave, breather wave and periodic lump solutions for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluid mechanics and plasma physics ⋮ Application of the homotopy perturbation method for the Fokker-Planck equation ⋮ Numerical study of modified Adomian's method applied to Burgers equation ⋮ An optimized decomposition method for nonlinear ordinary and partial differential equations ⋮ New applications of variational iteration method using Adomian polynomials ⋮ Bilinear auto-Bäcklund transformations and similarity reductions for a \((3+1)\)-dimensional generalized Yu-Toda-Sasa-Fukuyama system in fluid mechanics and lattice dynamics ⋮ Solution of the fully fuzzy linear systems using the decomposition procedure ⋮ Two-point iterative methods for solving nonlinear equations ⋮ Cosine expansion-based differential quadrature method for numerical solution of the KdV equation ⋮ Solitary wave solutions for the KdV and mKdV equations by differential transform method ⋮ The presentation of explicit analytical solutions of a class of nonlinear evolution equations ⋮ Solitary wave solutions of the improved KdV equation by VIM ⋮ New exact solutions for mCH and mDP equations by auxiliary equation method ⋮ New exact solutions and numerical approximations of the generalized KdV equation ⋮ Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method ⋮ A Legendre‐based approach of the optimized decomposition method for solving nonlinear Caputo‐type fractional differential equations ⋮ Single soliton and double soliton solutions of the quadratic‐nonlinear Korteweg‐de Vries equation for small and long‐times ⋮ Bilinear form, bilinear Bäcklund transformations, breather and periodic-wave solutions for a \((2+1)\)-dimensional shallow water equation with the time-dependent coefficients ⋮ Line-rogue waves, transformed nonlinear waves and their interactions for a \((3+1)\)-dimensional Korteweg-de Vries equation in a fluid ⋮ Mixed lump-stripe, bright rogue wave-stripe, dark rogue wave-stripe and dark rogue wave solutions of a generalized Kadomtsev-Petviashvili equation in fluid mechanics ⋮ Convergence of iterative methods applied to generalized Fisher equation ⋮ Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions ⋮ Homotopy perturbation method for modified Camassa-Holm and Degasperis-Procesi equations ⋮ Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation. ⋮ Approximate analytic solution for the KdV and Burger equations with the homotopy analysis method ⋮ Geometrical interpretation and approximate solution of non‐linear KdV equation ⋮ Solitonic fusion and fission for a \((3 + 1)\)-dimensional generalized nonlinear evolution equation arising in the shallow water waves ⋮ The Adomian decomposition method for solving partial differential equations of fractal order in finite domains ⋮ Bilinear auto-Bäcklund transformations and soliton solutions of a \((3+1)\)-dimensional generalized nonlinear evolution equation for the shallow water waves ⋮ Adomian decomposition method with modified Bernstein polynomials for solving ordinary and partial differential equations ⋮ An application of the modified Adomian decomposition method for (\(N + 1\))-dimensional sine-Gordon field ⋮ Solitary wave solutions of some nonlinear physical models using Riccati equation approach ⋮ Exact solutions for the generalized Klein-Gordon equation via a transformation and exp-function method and comparison with Adomian's method ⋮ Numerical solution for the Falkner-Skan equation ⋮ Analytical solution of variant Boussinesq equations ⋮ Rational solutions in Grammian form for the \((3+1)\)-dimensional generalized shallow water wave equation ⋮ A reliable technique for solving third‐order dispersion equations ⋮ Approximate Jacobi elliptic function solutions of the modified KdV equation via the decomposition method ⋮ A simple similarity-transformation-iterative scheme applied to Korteweg-de Vries equation ⋮ Variational iteration method for solving Burgers and coupled Burgers equations ⋮ Homotopy perturbation method for numerical solutions of KdV‐Burgers' and Lax's seventh‐order KdV equations ⋮ The solution of linear and nonlinear systems of Volterra functional equations using Adomian-Padé technique ⋮ Variational iteration method for modified Camassa-Holm and Degasperis-Procesi equations ⋮ The fractional variational iteration method improved with the Adomian series ⋮ An application of the modified decomposition method for the solution of the coupled Klein-Gordon-Schrödinger equation ⋮ On the convergence of He's variational iteration method ⋮ Modification of quintic B-spline differential quadrature method to nonlinear Korteweg-de Vries equation and numerical experiments ⋮ New solitary wave solutions of some nonlinear evolution equations with distinct physical structures ⋮ Natural frequencies of thin rectangular plates using homotopy-perturbation method ⋮ Modified decomposition method for nonlinear Volterra-Fredholm integral equations ⋮ Comparison differential transformation technique with adomian decomposition method for linear and nonlinear initial value problems ⋮ Numerical solution of the Laplace equation in annulus by adomian decomposition method ⋮ ADM-Padé technique for the nonlinear lattice equations ⋮ Application of the Adomian decomposition method for the Fokker-Planck equation ⋮ Exact and numerical soliton solutions of some nonlinear physical models ⋮ Approximate explicit solution of Camassa-Holm equation by He's homotopy perturbation method ⋮ Solitary wave solutions for the general KdV equation by Adomian decomposition method ⋮ Comparison study between restrictive Taylor, restrictive Padé approximations and Adomian decomposition method for the solitary wave solution of the general KdV equation ⋮ New soliton-like and periodic-like solutions for the KdV equation ⋮ Numerical doubly periodic solution of the KdV equation with the initial condition via the decomposition method ⋮ Exact multi-wave solutions for the KdV equation ⋮ Lump solutions to the Kadomtsev-Petviashvili equation
Cites Work
- A review of the decomposition method in applied mathematics
- Analytical approximations and Padé approximants for Volterra's population model
- Solving frontier problems of physics: the decomposition method
- Global solutions for the KdV equation with unbounded data
- A new algorithm for calculating Adomian polynomials for nonlinear operators
- The modified decomposition method and Padé approximants for solving the Thomas-Fermi equation
- The solution of the Boussinesq equation using the method of lines
- On nonanalytic solitary waves formed by a nonlinear dispersion.
- Soliton Solutions of Non-linear Evolution Equations
- The use of Backlund transformations in obtaining N-soliton solutions in Wronskian form
- Soliton solutions of the Korteweg de Vries and the Kadomtsev-Petviashvili equations: the Wronskian technique
- Soliton Interactions in Two Dimensions
- Periodic solutions of the KdV equation
- Compactons: Solitons with finite wavelength
- Theory of a Solid State Plasma Waveguide in a Transverse Magnetic Field
- Exact envelope-soliton solutions of a nonlinear wave equation
- Exact N-soliton solutions of the wave equation of long waves in shallow-water and in nonlinear lattices
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item