On non commutative sinh-Gordon Equation

TL;DR

This paper extends the sinh-Gordon equation into a noncommutative space, generalizing its linear system and Lax pair, resulting in a version with additional constraints and conserved currents.

Contribution

It introduces a novel noncommutative sinh-Gordon equation with a generalized Lax representation and conserved quantities, expanding the integrable systems framework.

Findings

Derived a noncommutative version of the sinh-Gordon equation

Generalized the linear system and Lax pair for noncommutative space

Identified conserved currents associated with the noncommutative extension

Abstract

We give a noncommutative extension of sinh-Gordon equation. We generalize a linear system and Lax representation of the sinh-Gordon equation in noncommutative space. This generalization gives a noncommutative version of the sinh-Gordon equation with extra constraints, which can be expressed as global conserved currents.