Classical Lie symmetries and reductions of a nonisospectral Lax pair

TL;DR

This paper applies classical Lie symmetry analysis to a 2+1 dimensional nonisospectral Lax pair, deriving reductions to 1+1 dimensions and clarifying the spectral parameter's role.

Contribution

It introduces a systematic Lie symmetry approach to reduce a nonisospectral problem, providing new insights into spectral problems in lower dimensions.

Findings

Derived new reductions to 1+1 dimensions

Clarified the role of the spectral parameter in reductions

Identified nontrivial spectral problems in lower dimensions

Abstract

The classical Lie method is applied to a nonisospectral problem associated with a system of partial differential equations in 2+1 dimensions (Maccari A, J. Math. Phys. 39, (1998), 6547-6551). Identification of the classical Lie symmetries provides a set of reductions that give rise to different nontrivial spectral problems in 1+1 dimensions. The form in which the spectral parameter of the 1+1 Lax pair is introduced is carefully described.