Interaction solutions to the (1+1)-dimensional generalized Drinfel'd-Sokolov-Wilson equation

摘要

In this paper, abundant interaction solutions for the (1 + 1)-dimensional generalized Drinfel'd-Sokolov-Wilson (gDSW) equation are presented. First, two groups of lumpsoliton-type interaction solutions are constructed by using a combination of quadratic function and two exponential functions. Especially, lump-twin soliton-type solution therein can generate rogue wave, which rarely appears in (1 + 1)-dimensional nonlinear systems in comparison with (2 + 1)-dimensional nonlinear systems. When certain parameters are taken to zero, these exact solutions are reduced to corresponding lump, soliton and lumpoff solutions. Second, the lump-periodic wave-type and soliton-periodic wave-type interaction solutions are also found on the basis of the bilinear form of gDSW equation. In the concrete analysis, we use mathematical software Maple to deal with some complicated symbolic computations. Figures are presented to show the dynamical features of these solutions.