Characteristic integrals and general solution of the Ferapontov-Shabat-Yamilov lattice

TL;DR

This paper provides a quadrature-free general solution and recurrent formulas for characteristic integrals of finite Ferapontov-Shabat-Yamilov lattices, based on determinantal equations, demonstrated on a two-component system.

Contribution

It introduces a novel, explicit method for solving and analyzing finite Ferapontov-Shabat-Yamilov lattices without quadratures, using determinantal equations.

Findings

Derived a general solution for the lattice system.

Established recurrent formulas for characteristic integrals.

Validated results with a two-component system example.

Abstract

For the finite (non-periodic) systems obtained from a lattice introduced by Ferapontov and independently by Shabat and Yamilov, we present a quadrature-free general solution and a recurrent formula for the characteristic integrals. The derivation of these formulae relies on the underlying determinantal equations. We illustrate the results using a two-component system.