Lie symmetry analysis of differential equations provides a powerful and fundamental
framework to the exploitation of systematic procedures leading to the integration by …

This review summarizes all known results (up to this date) about methods of integration of
the classical Lotka–Volterra systems with diffusion and presents a wide range of exact …

In this manuscript, the Lie point symmetries, conservation laws, and traveling wave
reductions have all been derived. Also, new forms of soliton solutions of generalized q …

In this paper, the nonlinear modified Gardner (mG) equation is under consideration which
represents the super nonlinear proliferation of the ion-acoustic waves and quantum electron …

A fourth-order nonlinear generalized Boussinesq water wave equation is studied in this
work, which describes the propagation of long waves in shallow water. We employ Lie …

The general concept of nonlinear self-adjointness of differential equations is introduced. It
includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self …

In the present paper, a new (3+ 1)-dimensional Schrödinger equation in Quantum
Mechanics is derived. Based on the extended (3+ 1)-dimensional zero curvature equation …

Nonlinear wave equations are generated by the elastic wave propagation through inelastic
material. We studied such a unidirectional nonlinear elastic wave by considering potential …

In this paper, a novel (3+ 1)-dimensional sine-Gorden and a sinh-Gorden equation are
derived. These two equations are derived for the first time from the extended (3+ 1) …

Under investigation in this work is a generalized higher-order beam equation, which is an
important physical model and describes the vibrations of a rod. By considering Lie symmetry …