Multidimensional linearizable system of $n$-wave type equations

TL;DR

This paper introduces a linearizable, completely integrable multidimensional system of n-wave type nonlinear PDEs, derived via spectral methods similar to the dressing method, and provides explicit solutions.

Contribution

It presents a novel linearizable version of multidimensional n-wave equations using spectral representation and dressing-like methods, expanding integrability techniques.

Findings

System is shown to be completely integrable

Particular solutions are explicitly constructed

Spectral representation underpins the linearization

Abstract

A linearizable version of multidimensional system of $n$-wave type nonlinear PDEs is proposed. This system is derived using the spectral representation of its solution via the procedure similar to the dressing method for the ISTM-integrable nonlinear PDEs. The proposed system is shown to be completely integrable, particular solution is represented.