Lattice equations and their solutions with complexity of polynomial class

TL;DR

This paper introduces new lattice equations with solutions of polynomial complexity, utilizing shift operators and binary trees to derive solutions for initial value problems in one-dimensional space.

Contribution

It proposes novel lattice equations with polynomial solution complexity and applies innovative methods like shift operators and binary trees for solution derivation.

Findings

Solutions have polynomial complexity class.

New lattice equations are introduced.

Methodology involves shift operators and binary trees.

Abstract

We discuss initial value problems for time evolution equations in one dimensional space which are expressed by the lattice operators and propose some new equations to which complexity of solutions is of polynomial class. Novel type of expressions using shift operators and binary trees are applied for the derivation of solution.