New dual-wave soliton solutions are addressed for the two-mode Sawada-Kotera (TmSK)
equation arising in fluids by the modified Kudryashov and new auxiliary equation methods …

In this work, we present a new two-mode version to the complex Hirota equation. This new
model arises in many applications in the field of optics, communications and other …

A new two-mode version of the generalized Zakharov-Kuznetsov equation is derived using
Korsunsky's method. This dynamical model describes the propagation of two-wave solitons …

The fractional diffusion and dispersion equations are reinterpreted in determining the effect
of fluid flow and displacement processes through certain compressible phenomena and …

In this paper we communicated with three different ansatze methods including the tanh-
expansion method, the rational sine–cosine method and the Kudryashov-expansion method …

In this paper, the evolutionary Cahn–Allen equation is upgraded into the generalized two-
mode version via Korsunsky's sense. The new established model is characterized in terms …

New two-mode version of the generalized Burger–Huxley equation is derived using
Korsunsky's operators. The new model arises in the applications of nerve fibers and liquid …

This study addresses dual-mode equations, focusing on the nonlinear wave behavior
characterized by simultaneous bidirectional movement influenced by a specific phase …

The two-mode Korteweg-de Vries (TMKdV) equation is a nonlinear dispersive wave model
that describes the motion of two different directional wave modes with the same dispersion …

The perturbed Boussinesq equation and the KdV-Caudrey-Dodd-Gibbon equation describe
the characteristics of longitudinal waves in bars, long water waves, plasma waves, quantum …