Application of exp-function method to Dullin-Gottwald-Holm equation

DOI10.1016/j.amc.2009.01.017zbMath1173.35666OpenAlexW2023811477MaRDI QIDQ1021560

Da-Quang Xian, Guang-Can Xiao, Xi-Qiang Liu

Publication date: 8 June 2009

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

Full work available at URL: https://doi.org/10.1016/j.amc.2009.01.017

zbMATH Keywords

solitary wave solutionexp-function methodDullin-Gottwald-Holm equationkink-wavebi-periodic traveling-wave solutionbounded-wave solutions

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Analyticity in context of PDEs (35A20) Soliton equations (35Q51) Solutions to PDEs in closed form (35C05)

Related Items (12)

Classification of bounded travelling wave solutions for the Dullin-Gottwald-Holm equation ⋮ Maximum principle for optimal distributed control of the viscous dullin-gottwald-Holm equation ⋮ New exact periodic wave solutions for the Dullin-Gottwald-Holm equation ⋮ Saddle-node heteroclinic orbit and exact nontraveling wave solutions for \((2 + 1)D\) KdV-Burgers equation ⋮ EXACT TRAVELING WAVE SOLUTIONS AND BIFURCATIONS FOR THE DULLIN-GOTTWALD-HOLM EQUATION ⋮ Existence of solitary solutions in a class of nonlinear differential equations with polynomial nonlinearity ⋮ Traveling wave solutions of generalized Dullin-Gottwald-Holm equation with parabolic law nonlinearity ⋮ 1-soliton solution and conservation laws of the generalized Dullin-Gottwald-Holm equation ⋮ Generalization of exp-function and other standard function methods ⋮ Be careful with the Exp-function method - additional remarks ⋮ Homoclinic breather-wave solutions and doubly periodic wave solutions for coupled KdV equations ⋮ New soliton and periodic wave solutions to the fractional DGH equation describing water waves in a shallow regime

Cites Work

• Unnamed Item
• Exp-function method for nonlinear wave equations
• On asymptotically equivalent shallow water wave equations
• Explicit and exact special solutions for BBM-like \(B(m,n)\) equations with fully nonlinear dispersion
• New exact special solutions with solitary patterns for Boussinesq-like \(B(m,n)\) equations with fully nonlinear dispersion
• An integrable shallow water equation with peaked solitons

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