Solitons of the vector KdV and Yamilov lattices

TL;DR

This paper explores vector generalizations of the lattice KdV and Yamilov equations, deriving N-soliton solutions using algebraic matrix properties to advance understanding of their integrable structures.

Contribution

It introduces a novel approach to obtain N-soliton solutions for vector lattice equations through algebraic matrix methods, expanding the class of solvable models.

Findings

Derived explicit N-soliton solutions for vector lattice KdV and Yamilov equations

Established algebraic matrix properties as a tool for integrable systems

Enhanced understanding of soliton structures in vector lattice equations

Abstract

We study a vector generalizations of the lattice KdV equation and one of the simplest Yamilov equations. We use algebraic properties of a certain class of matrices to derive the N-soliton solutions.