Partial Differential Equations in Applied Mathematics (Dec 2021)
On the solutions and conservation laws of the 2D breaking soliton equation of fluid mechanics
Abstract
In this article, we study two-dimensional generalized breaking soliton equation, which describes two-dimensional interchange of Riemann wave disseminating alongside y-axis with a long wave disseminating alongside x-axis. We derive Lie symmetry generators of this nonlinear partial differential equation and then utilize them to perform symmetry reductions. Travelling wave variables are used to obtain most general closed-form solutions of this equation by using two procedures. In addition, we compute the conserved vectors of this equation by engaging the classical Noether’s theorem.
