A five-dimensional solitary-wave first order nonlinear PDE integrable by dressing method

TL;DR

This paper introduces a new five-dimensional nonlinear first order matrix PDE that generalizes the (2+1)-dimensional N-wave equation, using a dressing method based on a linear integral equation.

Contribution

It presents a novel five-dimensional integrable PDE extending known lower-dimensional models, derived via a dressing method involving a linear integral equation.

Findings

Derivation of a five-dimensional integrable PDE

Generalization of the (2+1)-dimensional N-wave equation

Application of a dressing method based on a linear integral equation

Abstract

We derive a five-dimensional nonlinear first order matrix PDE which is a generalization of the completely integrable (2+1)-dimensional $N$-wave equation. Similar to the $\bar\partial$-problem, our algorithm is based on the linear integral equation of special form.