1+1 spectral problems arising from the Manakov-Santini system

TL;DR

This paper explores the spectral problem of the Manakov-Santini system, identifying symmetries and deriving reduced spectral problems in 1+1 dimensions, enhancing understanding of its integrable structure.

Contribution

It introduces a symmetry-based reduction method for the Lax pair of the Manakov-Santini system, resulting in new spectral problems in lower dimensions.

Findings

Identified point Lie symmetries of the Lax pair

Derived five spectral problems in 1+1 dimensions

Provided insights into the integrable structure of the system

Abstract

This paper deals with the spectral problem of the Manakov Santini system. The point Lie symmetries of the Lax pair have been identified. Several similarity reductions arise from these symmetries. An important benefit of our procedure is that the study of the Lax pair instead of the partial differential equations yields the reductions of the eigenfunctions and also the spectral parameter. Therefore, we have obtained five interesting spectral problems in 1+1 dimensions.