This article delves into the wave dynamics of the (3+ 1)-dimensional nonlinear model, which
serves as a representation of shallow water waves. This model finds relevance in …

Nonlinear wave equations emerge naturally in optics as well as fluid dynamics. It is
noteworthy that, an essential class of special solutions that satisfy the underlying equations …

Physics-informed machine learning (PIML) has established itself as a new scientific
paradigm which enables the seamless integration of observational data with partial …

This paper explores the application of the generalized double reduction method to the (1+ 1)-
dimensional Kaup–Boussinesq system, which models nonlinear wave propagation …

Lie group theory is applied to the curve equation which maintains constant normal
accelerations for a vehicle with constant deceleration. The curve equation is a third order …

This research article analytically investigates a soliton equation of high dimensions,
particularly with applications, and precisely in the fields of physical sciences and …

All low‐order conservation laws are found for a general class of nonlinear wave equations in
one dimension with linear damping which is allowed to be time‐dependent. Such equations …

In this study, we explore the invariance properties of a tumor growth model involving two
distinct cell populations. These populations are characterized by different diffusion …

In this paper, we study a viscous Cahn–Hilliard equation from the point of view of Lie
symmetries in partial differential equations. The analysis of this equation is motivated by its …

All energy-momentum type conservation laws are found for a general class of damped
nonlinear wave equations in one dimension. The classification shows that conservation laws …