Two Kinds of New Integrable Couplings of the Negative-Order Korteweg-de Vries Equation

Abstract EN

Based on some known loop algebras with finite dimensions, two different negative-order integrable couplings of the negative-order Korteweg-de Vries (KdV) hierarchy of evolution equations are generated by making use of the Tu scheme, from which the corresponding negative-order integrable couplings of the negative-order KdV equations are followed to be obtained.

The resulting Hamiltonian structure of one negative integrable coupling isderived from the variational identity.