The decomposition method for solving (2+1)-dimensional Boussinesq equation and (3+1)-dimensional KP equation

DOI10.1016/j.amc.2003.08.059zbMath1058.65111OpenAlexW1978920908MaRDI QIDQ1881711

Salah M. El-Sayed, Doǧan Kaya

Publication date: 14 October 2004

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2003.08.059

zbMATH Keywords

numerical examplesnonlinear evolution equationssolitary-wave solutionsKadomtsev-Petviashvili equation\((2+1)\)-dimensional Boussinesq equation\((3+1)\)-dimensional KP equationAdomian decomposition methods

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Abstract parabolic equations (35K90) Soliton equations (35Q51) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (14)

Blow-up solutions of the generalized Boussinesq equation obtained by variational iteration method ⋮ Similarity transformations and exact solutions for a family of higher-dimensional generalized Boussinesq equations ⋮ Rational and complexiton solutions of the \((3+1)\)-dimensional KP equation ⋮ Exact solitary wave solutions of the generalized \((2+1)\) dimensional Boussinesq equation ⋮ New families of travelling wave solutions for Boussinesq-Burgers equation and \((3+1)\)-dimensional Kadomtsev-Petviashvili equation ⋮ Application of Adomian decomposition method to bounded and unbounded Stokes' problems ⋮ Invariant solutions and conservation laws of the (2 + 1)-dimensional Boussinesq equation ⋮ Explicit periodic solitary wave solutions for the \((2+1)\)-dimensional Boussinesq equation ⋮ Asymptotic behavior of the periodic wave solution for the \((3+1)\)-dimensional Kadomtsev-Petviashvili equation ⋮ Comment on the \(3+1\) dimensional Kadomtsev-Petviashvili equations ⋮ Analytic studies and numerical simulations of the generalized Boussinesq equation ⋮ New explicit and exact traveling wave solutions of \((3+1)\)-dimensional KP equation ⋮ Exp-function method for solving Kuramoto-Sivashinsky and Boussinesq equations ⋮ On the study of oscillating viscous flows by using the Adomian-Padé approximation

Cites Work

• A review of the decomposition method in applied mathematics
• Solving frontier problems of physics: the decomposition method
• Symbolic computation and various exact solutions of potential Kadomtsev-Petviashvili equation.
• New soliton-like solutions to the potential Kadomtsev-Petviashvili (PKP) equation.
• An application of the decomposition method for the generalized KdV and RLW equations
• Comparing numerical methods for Helmholtz equation model problem.
• New solitonic solutions to a \((3+1)\)-dimensional Jimbo-Miwa equation
• Compactons dispersive structures for variants of the \(K(n,n)\) and the KP equations
• On the solution of the coupled Schrödinger-KdV equation by the decomposition method
• New explicit solitary wave solutions for \((2+1)\)-dimensional Boussinesq equation and \((3+1)\)-dimensional KP equation
• On the extended applications of homogeneous balance method
• On a generalized fifth order KdV equation
• Periodic Soliton Solutions as Imbricate Series of Rational Solitons: Solutions to the Kadomtsev-Petviashvili Equation with Positive Dispersion
• On the solution of a korteweg-de vries like equation by the decomposition method
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