The traveling wave solutions of a generalized HD type equation are investigated in this study. The traveling wave system is a singular system of the first class with given parameter conditions. From the standpoint of dynamical systems, the bifurcatio...
We consider the exact traveling wave solutions for the coupled nonlinear generalized Zakharov equations. By employing the method of dynamical systems, we are able to obtain bifurcations of the phase portraits of the corresponding planar dynamical sys...
In this paper, we apply a machine-learning approach to learn traveling solitary waves across various physical systems that are described by families of partial differential equations (PDEs). Our approach integrates a novel interpretable neural networ...
This paper studies the bifurcations of the exact solutions for the time–space fractional complex Ginzburg–Landau equation with parabolic law nonlinearity. Interestingly, for different parameters, there are different kinds of first integra...
In the areas of tidal and tsunami waves in oceans, rivers, ion and magneto-sound waves in plasmas, electromagnetic waves in transmission lines, homogeneous and stationary media, etc., the Riemann wave equations are attractive nonlinear equations. The...
The sinh-Gordon equation is simply the classical wave equation with a nonlinear sinh source term. It arises in diverse scientific applications including differential geometry theory, integrable quantum field theory, fluid dynamics, kink dynamics, and...
The dynamical wave solutions of the time–space fractional Date–Jimbo–Kashiwara–Miwa (DJKM) equation have been obtained in this article using an innovative and efficient technique including the Riccati–Bernoulli sub-ODE m...