Abstract:

We concentrate on the nonlinear wave solutions of the new (3+1)-dimensional KP equation, which was firstly proposed by Wazwaz in 2022. Based on the Hirota bilinear form, the $ P $-breathing solutions are mainly obtained from the $ N $-soliton solutions utilizing the module resonance technique. Then, using parameter limit approach, the Lump solutions are derived by degenerating behaviors of the homoclinic breathing solutions and $ N $-soliton solutions on the basis of the special relations of parameters. In addition, from the partial degeneration of the $ N $-soliton solutions, some hybrid solutions are investigated by the interaction solutions among the breathing, soliton and Lump solutions.

Key words: New (3+1)-dimensional KP equation, $ P $-Breathing solutions, Degeneration behaviors, $ Q $-Lump solutions, Hybrid solutions