Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions

Abstract

A list of forty third-order exactly integrable two-field evolutionary systems is presented. Differential substitutions connecting various systems from the list are found. It is proved that all the systems can be obtained from only two of them. Examples of zero curvature representations with $4\times 4$ matrices are presented.

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (3)

• Extending Hamiltonian Operators to Get Bi-Hamiltonian Coupled KdV Systems
• A Class of Coupled KdV systems and Their Bi-Hamiltonian Formulations
• Integrable Anisotropic Evolution Equations on a Sphere

Cited by in corpus (5)

• Integrable evolution equations with constant separant
• Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations
• Simplifications of Lax pairs for differential-difference equations by gauge transformations and (doubly) modified integrable equations
• On matrix Lax representations and constructions of Miura-type transformations for differential-difference equations
• Matrix Lax pairs under the gauge equivalence relation induced by the gauge group action and Miura-type transformations for lattice equations