Investigate the dynamic nature of soliton solutions and bifurcation analysis to a new generalized two-dimensional nonlinear wave equation with its stability

In this current research, we investigate a new generalized two-dimensional nonlinear wave equation of engineering physics using two versatile approaches. Nonlinear wave models are very important in that they play a key role in modeling diverse occurrences in cosmology, solid mechanics and fluid dynamics, astrophysics, mathematical physics and engineering. The research work is based on three steps. Firstly, soliton solutions are secured via the modified Sardar sub-equation method (MSSEM) and the generalized exponential rational function method (GERFM). Secondly, for bifurcation analysis phase portraits of an equation are erected. Also, using the Galilean transformation, the given equation plane dynamical system is erected and all possible phase portraits are provided. Lastly, the modulation instability of the equation is examined. In order to better comprehend how the nonlinear wave equation depicts physical processes, the wave dynamics of the solutions are displayed to give the results a more physical perspective. The use of these findings in physics, engineering and complex media is essential.

Automated summary

In this research, a new generalized two-dimensional nonlinear wave equation is investigated using two versatile approaches. Nonlinear wave models play a key role in various fields such as physics, engineering, and complex media. The research involves obtaining soliton solutions, constructing bifurcation analysis phase portraits, and examining the modulation instability of the equation.