The classical Lonngren wave equation, identified as the notable equation in electronics due to its importance in nonlinear and dispersive media. It simulates propagation of electrical signals in semi-conductor materials, notably tunnel diodes. The Sardar sub-equation method is implemented in this paper for the extraction of new forms of soliton solutions. The solitonsolutions of the given model are obtained under the assumption of an exact evaluation of the system’s unknowns. Computational analysis, carried out with Mathematica, provides a robust framework for the investigation of these nonlinear structures. A broad range of exact solutions, encompassing bright and singular solitons, originated out of the obtained solutions. To enhance the physical manifestation of the solutions, multiple 2D, 3D, and contour plots are generated with specific parameter values. Numerical validation is also performed to confirm tha accuracy of analytical results. Furthermore, using tools such as Lyapunov exponents, phase diagrams, time series, Poincaré maps, and the power spectrum, a deep dynamical assessment delves into the bifurcation patterns and chaotic behavior. Accordingly, the obtained results have important implications on the dynamics of nonlinear wave propagation and demonstrated that the SSM method yields exact solutions of the analytical type.
Farooq et al. (Fri,) studied this question.