Acoustics Wave Dynamics of the Soliton Solutions of the Nonlinear Dissipative Zabolotskaya–Khokhlov Equation

In this manuscript, we derive soliton solutions for the (2 + 1)-dimensional nonlinear dissipative Zabolotskaya-Khokhlov equation. This equation addresses nonlinear effects in stratified media and controls the diffraction of sound beam propagation. The dynamical wave solutions are generated by using the bilinear neural network method. These solutions are composed by the specific activation functions of single-layer "3-3-1" model, to obtain the breather wave and lump wave soliton solutions. Meanwhile, a "3-4-1" a model is used to derive the lump wave interaction with the double exponential functions. Moreover, the double-layer model activation function "3-3-4-1" is considered to get the rough wave solitons, while a "3-2-2-1" model is applied to construct the periodic wave. The symbolic computational software Maple is used to verify these solutions and to draw plots for the physical interpretation. The graphical visualization of these solutions is shows in the form of three-dimensional, line and density plots. These results may shed some light in our understanding of the nonlinear dissipative Zabolotskaya-Khokhlov equation.