Weak Transversality and Partially Invariant Solutions

TL;DR

This paper introduces new exact solutions for complex nonlinear physical equations using symmetry group methods, especially when traditional Lie symmetry reduction is not feasible.

Contribution

It develops solution techniques leveraging symmetry groups for nonlinear equations where standard methods fail, expanding the toolkit for solving such systems.

Findings

Derived new solutions for Navier-Stokes and Euler equations

Extended symmetry methods to cases where Lie reduction is inapplicable

Provided solutions for nonlinear Schroedinger and fluid systems

Abstract

New exact solutions are obtained for several nonlinear physical equations, namely the Navier-Stokes and Euler systems, an isentropic compressible fluid system and a vector nonlinear Schroedinger equation. The solution methods make use of the symmetry group of the system in situations when the standard Lie method of symmetry reduction is not applicable.