Linearisation of the (M,K)-reduced non-autonomous discrete periodic KP equation

TL;DR

This paper linearizes the (M,K)-reduced non-autonomous discrete KP equation on an algebraic curve's Picard group and constructs theta function solutions for specific initial value problems.

Contribution

It introduces a novel linearization approach for the discrete KP equation on algebraic curves and provides explicit theta function solutions.

Findings

Linearization of the (M,K)-reduced non-autonomous discrete KP equation on algebraic curves.

Construction of theta function solutions for specific initial value problems.

Demonstration of the method's applicability to special discrete KP equations.

Abstract

The (M,K)-reduced non-autonomous discrete KP equation is linearised on the Picard group of an algebraic curve. As an application, we construct theta function solutions to the initial value problem of some special discrete KP equation.