Abstract The (2+ 1)-dimensional Chaffee–Infante has a wide range of applications in
science and engineering, including nonlinear fiber optics, electromagnetic field waves …

In this work, we consider the ill-posed Boussinesq equation which arises in shallow water
waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is …

Different approaches to construct first integrals for ordinary differential equations and
systems of ordinary differential equations are studied here. These approaches can be …

The propagation of shallow water waves with small amplitudes as they propagate in a water
channel of constant depth at a uniform speed is described by general Boussinesq equation …

The equation for fluid flow in porous media is analyzed in this paper with the aid of Lie
symmetry method (LSM) and invariant subspace method (ISM). Infinitesimal generators, the …

In this paper, we obtain conservation laws of (2+ 1) dimensional Calogero–Bogoyavlenskii–
Schiff equation by non‐local conservation theorem method. Besides, exact solutions are …

In this work, we study the integrability aspects of the Schamel–Korteweg–de Vries equation
that play an important role in studying the effect of electron trapping on the nonlinear …

In this paper, the conservation laws, significant symmetries' application, and traveling wave
solutions are obtained for Burger–Fisher equation (BFE). Conservation laws have a great …

The Lie symmetry analysis is applied to study the Ablowitz–Kaup–Newell–Segur (AKNS)
system of water wave model. The AKNS system can be obtained from a dispersive-wave …

Compactons were introduced as solutions of nonlinear dispersive partial differential
equations. There exists a variety of third-order equations that support compacton solutions …