Derivation of some bi-wave solutions for a new two-mode version of the combined Schamel and KdV equations

This paper introduces novel findings in the investigation of new two-mode version of the combined Schamel and KdV equations. The proposed model demonstrates the dynamics of two waves concurrently propagating in different media such as nonlinear optics and plasma physics. The wave amplitudes, known also as modes, of these waves are dependent upon the interplay between the nonlinearity and dispersion parameters. While as, their wave-width are governed by the phase velocity parameter. By studying these fundamental aspects, our study introduces fresh insights into the behavior of the new two-mode model. The obtained results contribute to a deeper understanding of wave propagation phenomena in related fields of research.