Theoretical examination and simulations of two nonlinear evolution equations along with stability analysis

Abstract

Nonlinear evolution equations are employed in the representation of diverse intricate physical events, and the identification of precise solutions for these equations holds significance about their practical implementations. One of the significant challenges is the identification of traveling wave solutions inside established nonlinear evolution systems in the field of mathematical physics. In the present research, we employ the modified sub-equation approach, a very effective and strong technique, to ensure the solutions for the Klein–Gordon featuring cubic nonlinearity and Zakharov Kuznetsov–Benjamin Bona Mahony equations. Several restriction requirements that ensure the existence of these solutions are emphasized. By employing a linearization technique, we ascertain the stability gain. This methodology acquires original precise solutions of soliton nature. Furthermore, the nonlinear wave structures of both equations are illustrated through the consideration of several three-dimensional and two-dimensional plots. These plots are generated by selecting appropriate values for the parameters. It is expected that these innovative solutions would facilitate an in-depth understanding of the evolution and fluidity of these models. The solutions obtained comprise periodic functions, mixed periodic functions, rational solutions, and exponential solutions.

Keywords

• (1+1).dimensional Klein–Gordon equation
• Zakharov–Kuznetsov Benjamin–Bona Mahony
• Modified sub-equation method
• Stability analysis
• Exact solution