Combination of inverse spectral transform method and method of characteristics: deformed Pohlmeyer equation

TL;DR

This paper develops a novel approach combining inverse spectral transform and method of characteristics to analyze a four-dimensional nonlinear PDE system, unifying integrable models like the Pohlmeyer equation.

Contribution

It introduces a combined method for solving complex PDEs that include both inverse spectral and characteristic integrable reductions, expanding analytical tools for high-dimensional nonlinear systems.

Findings

Unified framework for inverse spectral and characteristic methods

New reductions of the four-dimensional PDE system

Potential applications to integrable models in mathematical physics

Abstract

We apply a version of the dressing method to a system of four dimensional nonlinear Partial Differential Equations (PDEs), which contains both Pohlmeyer equation (i.e. nonlinear PDE integrable by the Inverse Spectral Transform Method) and nonlinear matrix PDE integrable by the method of characteristics as particular reductions. Some other reductions are suggested.