Construction of exact solutions of nonlinear PDE via dressing chain in 3D

TL;DR

This paper introduces a novel method for constructing explicit solutions to nonlinear PDEs using dressing chains in 3D, leveraging dualities with lattice systems and finite reductions.

Contribution

It presents a new coupled system related to Toda lattices, an algorithm for explicit solution construction, and applies these to systems connected with the Volterra lattice.

Findings

New coupled system related to Toda lattices

Algorithm for explicit solutions via finite reductions

Examples of solutions for Volterra-related systems

Abstract

The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. A new coupled system related to the recently found lattice is presented. A method for eliminating nonlocalities in coupled systems by virtue of special finite reductions of the lattices is suggested. An original algorithm for constructing explicit solutions of the coupled systems based on the finite reduction of the corresponding lattice is proposed. Some new solutions for coupled systems related to the Volterra lattice are presented as illustrative examples.