Long-time asymptotics for an integrable evolution equation with a $3 \times 3$ Lax pair

TL;DR

This paper develops a Riemann-Hilbert framework to analyze the long-time behavior of solutions to an integrable nonlinear evolution equation characterized by a 3x3 Lax pair, advancing understanding of its asymptotic properties.

Contribution

The paper introduces a novel Riemann-Hilbert approach for deriving long-time asymptotics of a specific integrable equation with a 3x3 Lax pair, expanding analytical tools in integrable systems.

Findings

Derived a Riemann-Hilbert representation for the solution.

Obtained explicit formulas for long-time asymptotics.

Enhanced analytical understanding of the integrable equation's behavior.

Abstract

We derive a Riemann--Hilbert representation for the solution of an integrable nonlinear evolution equation with a $3 \times 3$ Lax pair. We use the derived representation to obtain formulas for the long-time asymptotics.