Weak Transversality and Partially Invariant Solutions

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.

23 pages, preprint CRM-2843

References in corpus (2)

• Group foliation and non-invariant solutions of the heavenly equation
• Partial Lie-point symmetries of differential equations

Cited by in corpus (8)

• On the geometry of lambda-symmetries, and PDEs reduction
• On the relation between standard and $\mu$-symmetries for PDEs
• On the notion of conditional symmetry of differential equations
• Asymptotic symmetries of difference equations on a lattice
• Computation of Partially Invariant Solutions for the Einstein Walker Manifolds' Identifying Equations
• Conditional symmetries and Riemann invariants for inhomogeneous hydrodynamic-type systems
• Reduction and Exact Solutions of the Ideal Magnetohydrodynamic Equations
• A Discussion on the Different Notions of Symmetry of Differential Equations