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arXiv · 1010.2075

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

Supaporn Suksern
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Abstract

Some solutions for one class of nonlinear fourth-order partial differential equations \[u_{tt} = ({κu + γu^2})_{xx} + νuu_{xxxx} + μu_{xxtt} + αu_x u_{xxx} + βu_{xx}^2 \] 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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Supaporn Suksern. 2010-10-11. Solutions for one class of nonlinear fourth-order partial differential equations. https://arxiv.org/abs/1010.2075

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