Ran Wang1, Xuegang Yuan1,2, Hongwu Zhang1, Jing Zhang3, Na Lv2,*
CMC-Computers, Materials & Continua, Vol.55, No.2, pp. 345-357, 2018, DOI:10.3970/cmc.2018.00233
Abstract In this paper, a nonlinear wave equation with variable coefficients is studied, interestingly, this equation can be used to describe the travelling waves propagating along the circular rod composed of a general compressible hyperelastic material with variable cross-sections and variable material densities. With the aid of Lou’s direct method1, the nonlinear wave equation with variable coefficients is reduced and two sets of symmetry transformations and exact solutions of the nonlinear wave equation are obtained. The corresponding numerical examples of exact solutions are presented by using different coefficients. Particularly, while the variable coefficients are taken as some special constants, the nonlinear… More >
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