Solutions for one class of nonlinear fourth-order partial differential equations

2010/10/11 by Supaporn Suksern, Suksern, Supaporn
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1010.2075

openalex publication_date 2010/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Some solutions for one class of nonlinear fourth-order partial differential equations u_tt = (κu + γu²)_xx + νuu_xxxx + μu_xxtt + αu_x u_xxx + βu_xx² where α, β, γ, μ, ν and κ are arbitrary constants are presented in the paper. This equation may be thought of as a fourth-order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Furthermore, this equation is a Boussinesq-type equation which arises as a model of vibrations of harmonic mass-spring chain. The idea of travelling wave solutions and linearization criteria for fourth-order ordinary differential equations by point transformations are applied to this problem.

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