Steeping and dispersive effects analysis of a couple of long-wave equations in dispersive media

Abstract

Dispersive wave propagations are described by nonlinear models, such as regularized long waves and modified regularized long waves, where nonlinearity and dispersion are important aspects of wave evolution to model long-wave propagation in dispersive media with small amplitudes. In this article, solitary wave solutions to the formerly indicated nonlinear equations are computed as exponential, hyperbolic, and trigonometric structures and their integration by balancing the steeping and dispersion terms of the highest order, and different classes of definitive localized coherent structures with their interaction properties, such as soliton solutions, are extracted by assigning appropriate functions. We have also investigated the impact of steeping and wave spread on waveforms. The wave solutions are assessed using the enhanced modified simple equation approach, which organizes the soliton solutions based on the features of the dispersive interconnections with the nonlinear cubic and quadratic characters that exist in the equations. The consistent 3D and 2D soliton configurations show that the wave profile is modulated by the wave velocity function and the parameters associated with it, and most of the modulation is due to linear effects.