SOLUTIONS FOR ONE CLASS OF NONLINEAR FOURTHORDER PARTIAL DIFFERENTIAL EQUATIONS
Keywords:
Linearization problem, point transformation, nonlinear ordinary differential equation, travelling wave solutionAbstract
where α, β, , , v and are arbitrary constants are presented in the paper. This equation may bethought of as a fourth-order analogue of a generalization of the Camassa-Holm equation, in which there has been considerable interest recently. Furthermore, this equation is a Boussinesq-typeequation 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 is applied to this problem.
References
Clarkson, P.A. and Priestley, T.J. (1999).Symmetries of a class of nonlinear fourth order partial differential equations, J. Nonlinear Math., Phy. 6:66-98.
Clarkson, P.A., Mansfield, E.L., and Priestley,T.J. (1997). Symmetries of a class of nonlinear third order partial differential Equations, Math. Computer. Model.,25(8-9):195-212.
Ibragimov, N.H., Meleshko, S.V., andSuksern, S. (2008). Linearization of fourth-order ordinary differential Equations by point transformations. J.Phys. A: Math. Theor., 41(235206):19.
