Degeneration of solitons for a (3+1)-dimensional generalized nonlinear evolution equation for shallow water waves

A (3 + 1)-dimensional generalized shallow water waves equation is investigated with different methods. Based on symbolic computation and Hirota bilinear form, N-soliton solutions are constructed. In the process of degeneration of N-soliton solutions, T-breathers are derived by taking complexication method. Then rogue waves will emerge during the degeneration of breathers by taking the parameter limit method. Through full degeneration of N-soliton, M-lump solutions are derived based on long-wave limit approach. In addition, we also find out that the partial degeneration of N-soliton process can generate the hybrid solutions composed of soliton, breather and lump.

Automated summary

A (3+1)-dimensional generalized shallow water waves equation is investigated using different methods. N-soliton solutions, T-breathers, rogue waves, and M-lump solutions are derived through degeneration and parameter limit methods. Furthermore, hybrid solutions composed of soliton, breather, and lump are found during the partial degeneration process of N-soliton.