A constructive approach to the soliton solutions of integrable quadrilateral lattice equations

Abstract

Scalar multidimensionally consistent quadrilateral lattice equations are studied. We explore a confluence between the superposition principle for solutions related by the Backlund transformation, and the method of solving a Riccati map by exploiting two kn own particular solutions. This leads to an expression for the N-soliton-type solutions of a generic equation within this class. As a particular instance we give an explicit N-soliton solution for the primary model, which is Adler's lattice equation (or Q4).

22 pages

References in corpus (1)

• Linear quadrilateral lattice equations and multidimensional consistency

Cited by in corpus (7)

• Rational Solutions to the ABS List: Transformation Approach
• On Elliptic Lax Systems on the Lattice and a Compound Theorem for Hyperdeterminants
• Rational Solutions of the H3 and Q1 Models in the ABS Lattice List
• Elliptic (N,N^\prime)-Soliton Solutions of the lattice KP Equation
• Algebro-geometric integration of the Q1 lattice equation via nonlinear integrable symplectic maps
• A discrete Darboux-Lax scheme for integrable difference equations
• Soliton Fay identities. I. Dark soliton case