Construction of Multi-wave Solutions of Nonlinear Equations with Variable Coefficients Arising in Fluid Mechanics

The nonlinear development equations play an important role in describing natural phenomena, so it is very important to solve the nonlinear development equations. In this paper, the (2+1)-dimensional variable coefficient Date-Jimbo-Kashiwara-Miwa equation, and the variable coefficient shallow water wave equation are studied by using exp-function method, which can be regarded as a special multi-soliton method. The one-wave solution, two-wave solution, three-wave solution and four-wave solution are solved with the mathematical software Maple, and corresponding figures are drawn to better observe the state of the solution.