Soliton solutions and the interaction behaviour of the (3+1)-dimensional Jimbo-Miwa-like equation

Abstract

Abstract In this article, we aim to study the dynamical behavior of the (3+1)-dimensional Jimbo-Miwa-like (JML) equation. By using different methods, different forms of solutions are obtained. At the same time, in the same method, we also study the influence of parameters on the solution by changing the values of parameters. Firstly, we use the bilinear method to obtain the Y-type and X-type soliton solutions. Secondly, using different test functions, we obtain the interaction phenomenon between the solutions, which is obtained by a lump solution and a kink wave solution or by a lump solution and multi-kink wave solutions. Lastly, on the basis of the study of the single lump solution, we have made a further exploration. We not only obtain the lump-periodic solution, which verifies the periodicity, but also obtain the lump-soliton solution. For the above wave solutions, we graphically describe their dynamical properties with MAPLE. It is worth mentioning that the content of our study is different from the existing research: we not only use different methods to study the solutions of the JML equation, but also use different parameter relations and different values of parameters to study the changes of solutions. At the same time, we also use different test functions to study the same form of wave solutions. It is intuitive to see the influence of the test function on the dynamic behavior of the solution. In addition, our results not only enable us to understand the dynamic properties of such equations more intuitively, but also provide some ideas for researchers to facilitate more indepth exploration.