Reductions and new exact solutions of ZK, Gardner KP, and modified KP equations via generalized double reduction theorem

DOI10.1155/2013/340564zbMath1293.35066OpenAlexW2106691856WikidataQ58915973 ScholiaQ58915973MaRDI QIDQ2015377

Zulfiqar Ali, Imran Naeem, Rehana Naz

Publication date: 23 June 2014

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/340564

zbMATH Keywords

conservation lawsLie symmetriesZakharov-Kuznetsov equationmultiplier approachGardner Kadomtsev-Petviashvili equationmodified KP equations

Mathematics Subject Classification ID

Solutions to PDEs in closed form (35C05) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items (10)

Conservation laws and line soliton solutions of a family of modified KP equations ⋮ Numerical approximations and conservation laws for the sine-Gordon equation ⋮ Reductions and exact solutions of the \((2+1)\)-dimensional breaking soliton equation via conservation laws ⋮ Conservation laws for a Boussinesq equation. ⋮ Symmetry multi-reduction method for partial differential equations with conservation laws ⋮ Conservation laws, symmetries, and line soliton solutions of generalized KP and Boussinesq equations with \(p\)-power nonlinearities in two dimensions ⋮ Comparison of different approaches to construct first integrals for ordinary differential equations ⋮ Line-solitons, line-shocks, and conservation laws of a universal KP-like equation in 2+1 dimensions ⋮ Lie point symmetries, conservation laws and exact solutions of electrical transmission line model ⋮ Optimal subalgebra of GKP by using Killing form, conservation law and some more solutions

Cites Work

• Unnamed Item
• Unnamed Item
• Generalized solitary and periodic wave solutions to a \((2+1)\)-dimensional Zakharov-Kuznetsov equation
• The sine-cosine method for obtaining solutions with compact and noncompact structures
• Generalization of the double reduction theory
• Double reduction of PDEs from the association of symmetries with conservation laws with applications
• Conservation laws and conserved quantities for laminar two-dimensional and radial jets
• On double reductions from symmetries and conservation laws
• Non-local symmetries and conservation laws for one-dimensional gas dynamics equations.
• Relationship between symmetries and conservation laws
• A sine-cosine method for handling nonlinear wave equations
• Multiple structures of two-dimensional nonlinear Rossby wave
• Conservation laws and exact solutions of a class of non linear regularized long wave equations via double reduction theory and Lie symmetries
• Comparison of different approaches to conservation laws for some partial differential equations in fluid mechanics
• Solitons and singular solitons for the Gardner-KP equation
• Solitary wave solutions for the modified Kadomtsev-Petviashvili equation
• Sine-cosine method for finding the soliton solutions of the generalized fifth-order nonlinear equation
• The association of non-local symmetries with conservation laws: applications to the heat and Burgers' equations
• The first-integral method to study the Burgers–Korteweg–de Vries equation
• A Basis of Conservation Laws for Partial Differential Equations

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