Conservation laws of some lattice equations
Jun-wei Cheng, Da-jun Zhang
TL;DR
This paper derives an infinite number of conservation laws for various multi-dimensionally consistent lattice equations using their Lax pairs, highlighting their integrability properties.
Contribution
It introduces a systematic method to obtain conservation laws for several important lattice equations from their Lax pairs.
Findings
Infinite conservation laws derived for multiple lattice equations
Demonstrates integrability of these lattice systems
Provides a unified approach to conservation laws in lattice models
Abstract
We derive infinitely many conservation laws for some multi-dimensionally consistent lattice equations from their Lax pairs. These lattice equations are the Nijhoff-Quispel-Capel equation, lattice Boussinesq equation, lattice nonlinear Schr\"{o}dinger equation, modified lattice Boussinesq equation, Hietarinta's Boussinesq-type equations, Schwarzian lattice Boussinesq equation and Toda-modified lattice Boussinesq equation.
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