A Lax Operator Hierarchy for the New Fifth Order Integrable System

Darboux Transformations for a Lax Integrable System in 2n-Dimensions

A 2n-dimensional Lax integrable system is proposed by a set of specific spectral problems. It contains Takasaki equations, the self-dual Yang-Mills equations and its integrable hierarchy as examples. An explicit formulation of Darboux transformations is established for this Lax integrable system. The Vandermonde and generalized Cauchy determinant formulas lead to a description for deriving expl...

Negative order MKdV hierarchy and a new integrable Neumann-like system

The purpose of this paper is to develop the negative order MKdV hierarchy and to present a new related integrable Neumann-like Hamiltonian flow from the view point of inverse recursion operator and constraint method. The whole MKdV hierarchy both positive and negative is generated by the kernel elements of Lenard’s operators pair and recursion operator. Through solving a key operator equation, ...

The Lax Pair for the Mkdv Hierarchy

— In this paper we give an algorithmic method of deriving the Lax pair for the modified Korteweg-de Vries hierarchy. For each n, the compatibility condition gives the n-th member of the hierarchy, rather than its derivative. A direct consequence of this is that we obtain the isomonodromy problem for the second Painlevé hierarchy, which is derived through a scaling reduction. Résumé (La paire de...

Lax Operator for the Quantised Orthosymplectic

A new hierarchy of integrable systems associated to Hurwitz spaces.

In this paper, we introduce a new class of integrable systems, naturally associated to Hurwitz spaces (spaces of meromorphic functions over Riemann surfaces). The critical values of the meromorphic functions play the role of "times". Our systems give a natural generalization of the Ernst equation; in genus zero, they realize the scheme of deformation of integrable systems proposed by Burtsev, M...

A new integrable hierarchy, parametric solution and traveling wave solution

This paper gives a new integrable hierarchy of nonlinear evolution equations. In this hierarchy there are the following representative equations: ut = ∂ 5 xu − 2 3 , ut = ∂ 5 x (u 1 3 )xx − 2(u 1 6 )x u ; uxxt + 3uxxux + uxxxu = 0. The first two are in the positive order hierarchy while the 3rd one is in the negative order hierarchy. The whole hierarchy is shown integrable through solving a key...