Abstract
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.
Highlights
A the (3+1)-dimensional generalized nonlinear evolution equation for the shallow water waves is investigated with different methods
Through full degeneration of N -soliton, M -lump solutions are derived based on long wave limit approach
N -soliton solutions are constructed based on symbolic computation and Hirota bilinear form
Summary
We mainly investigate the (3+1)-dimensional generalized nonlinear evolution equation for the shallow water waves [35,36], the equation reads l1uxz + (l2ut + l3uxxx + l4uux)y + l5(ux∂x−1uy)x = 0. Based on the previous researches, we mainly investigate the deformation behaviors of N -soliton, most of solutions solutions obtained for Eq(1) are new and may be very meaningful to explain some special nonlinear science phenomenon.
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