Author(s)

Yin Ji, Xiyu Tan^*

College of Mathematics and Statistics, Jishou University, Jishou, China.

By employing the Hirota’s bilinear method and different test functions, the breather solutions of HSI equation with different structures are obtained based on symbolic calculation with perturbation parameters. Some new lump solitons are found in the process of studying the degradation behavior of breather solutions. The interaction between lump solution and soliton solution is constructed in the form of lump solution, and the motion trajectory of lump is obtained. In addition, the theorem of lump solitons and N-solitons superposition is given and proved. The superposition formula of lump is derived from the theorem, and its spatial evolution behavior is given.

HSI Equation, Breather-Waves, Lump Solutions, Interaction Solution

Ji, Y. and Tan, X. (2024) New Lump Solution and Their Interactions with N-Solitons for a Shallow Water Wave Equation. Journal of Applied Mathematics and Physics, 12, 2836-2848. doi: 10.4236/jamp.2024.128169.