Controllable rogue waves in a compressible hyperelastic plate

Abstract

In this paper, we investigate various rational solutions of a (2+1)-dimensional nonlinear equation with variable-coefficients which can describe the propagation of nonlinear waves in a compressible hyperelastic plate, and interestingly we find a new phenomenon in nonlinear hyperelastic mechanics—rogue waves. Based on the symmetry transformation and Hirota bilinear form, we obtain breather waves and rogue waves. And when we choose appropriate material parameters and transformation functions, we can control their directions of propagation. In addition, we present three new interaction solutions, i.e. the rogue waves keep moving from side to side between a pair of resonance stripe solitary waves. Finally, we analysis the dynamics characteristics and evolution behaviors of the obtained solutions by three-dimensional dynamic images. This paper exhibits the existence of rogue waves in nonlinear hyperelastic mechanics, and presents potential application value for control of rogue waves in elastic mechanics, fluid dynamics and other fields of nonlinear science.