Chen Lee Liu Equation Research Articles

A Liouville integrable Hamiltonian system associated with a generalized Kaup–Newell spectral problem

Starting from a generalized Kaup–Newell spectral problem involving an arbitrary function, we derive a hierarchy of nonlinear evolution equations, which is explicitly related to many important equations such as Kaup–Newell equation, Chen–Lee–Liu equation, Gerdjikov–Ivanov equation, Burgers equation, modified Korteweg–de Vries equation and Sharma–Tasso–Olever equation. It is also shown that the hierarchy is integrable in Liouville's sense and possesses multi-Hamiltonian structure.

Gauge transformations of constrained KP flows: New integrable hierarchies

Integrable systems in 1+1 dimensions arise from the KP hierarchy as symmetry reductions involving square eigenfunctions. Exploiting the residual gauge freedom in these constraints new integrable systems are derived. They include generalizations of the hierarchy of the Kundu–Eckhaus equation and higher-order extensions of the Yajima–Oikawa and Melnikov hierarchies. Constrained modified KP flows yield further integrable equations such as the hierarchies of the derivative NLS equation, the Gerdjikov–Ivanov equation, and the Chen–Lee–Liu equation.