Solving the Variable Coefficient Nonlinear Partial Differential Equations Based on the Bilinear Residual Network Method

In this work, a variable coefficient bilinear residual network method is proposed to solve nonlinear partial differential equations with variable coefficient, including two types of neural network models: 2–2 and 3–3. Various soliton solutions of a (2+1)-dimensional coupled nonlinear equation with variable coefficients are presented based on the variable coefficient bilinear residual network method. The interaction between lump wave and solitons is discussed through a mixed function of rational and exponential functions. Finally, the interaction between lump wave and periodic wave is analyzed through a mixed function of rational and trigonometric functions. Meanwhile, some three-dimensional and density maps are used to describe the dynamic properties of the obtained results.