Third Order Integrable Equation Possessing Symplectic Operator Of Degree 9

Abstract

We perform a classification of third order integrable systems of evolution equations with respect to higher symmetries. Applying it, we consider polynomial systems that are 0-homogeneous under a suitable weighting of variables with main matrix $\ast \ast \ast$ having a seventh-order symmetry. A new integrable equation is discovered. For this new supersymmetric equation the Lax representation and bi-Hamiltonian structures are given.

16 pages

References in corpus (3)

• The Integrability of New Two-Component KdV Equation
• A fifth-order bi-Hamiltonian system
• On the classification of fifth-order integrable systems