Peakons and compactons of the (2+1)-dimensional modified dispersive water-wave system

Abstract

For a higher-dimensional nonlinear dynamical system, there exist abundant coherent excitations. The variable-separated method is a powerful approach to deriving these structures, as its solutions allow for arbitrary functions. Previous works have produced numerous results, including solitons, chaos and fractals. As the molecule structure appears, constructing the multi-soliton molecule through this technology is a meaningful work, especially considering the local peakons and compactons that were seldom discussed before. In this paper, after taking the Bäcklund transformation, the variable-separated solution for the (2+1)-dimensional modified dispersive water-wave system is first derived, which is an important physical model in describing the nonlinear and dispersive long gravity waves. As a result, the multi-peakons and multi-compactons are constructed through the derived universal formula with the aid of the variable functions p and q. These solitons include two general clusters of M × N peakons and compactons, from which the multi-soliton molecules and their interactions are presented.