Multi-lump or lump-type solutions to the generalized KP equations in (N+1)-dimensions

Authors：Cheng, Li^*; Zhang, Yi; Ma, Wen-Xiu; Ge, Jian-Ya

Source：EUROPEAN PHYSICAL JOURNAL PLUS, 2020, 135(4): 379.

DOI：10.1140/epjp/s13360-020-00366-z

• BACKLUND TRANSFORMATION
• KADOMTSEV-PETVIASHVILI
• SOLITONS
• WAVE

We aim to explore lump or lump-type solutions to the generalized Kadomtsev-Petviashvili (gKP) equations in (N+1)-dimensions via the long wave limit technique. The construction procedure for presenting lump or lump-type solutions is improved. The key step is that all the involved parameters are extended to the complex field. We first furnish lump solutions from the corresponding soliton solutions to the (2+1)-dimensional gKP equation. In particular, a general class of multi-lump solutions of the (2+1)-dimensional gKP equation can be obtained. It is then shown that there exist lump-type solutions to the (N+1)-dimensional gKPI equations with N >= 3 by means of the improved long wave limit technique.

• Institution
  西北大学; 浙江师范大学