Addition formulae, B\"acklund transformations, periodic solutions and quadrilateral equations
Danda Zhang, Da-jun Zhang
TL;DR
This paper uses addition formulae of trigonometric and elliptic functions to derive B"acklund transformations and quadrilateral equations, leading to periodic solutions for multidimensionally consistent equations.
Contribution
It introduces a novel method connecting addition formulae with B"acklund transformations and quadrilateral equations for integrable systems.
Findings
Derived B"acklund transformations from addition formulae.
Generated periodic solutions for multidimensional quadrilateral equations.
Established connections between elliptic functions and integrable lattice equations.
Abstract
Addition formulae of trigonometric and elliptic functions are used to generate B\"acklund transformations together with their connecting quadrilateral equations. As a result we obtain periodic solutions for a number of multidimensionally consistent affine linear and multiquadratic quadrilateral equations.
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Taxonomy
TopicsNonlinear Waves and Solitons · Matrix Theory and Algorithms · Numerical methods for differential equations