A completely integrable system and parametric representation of solutions of the Wadati-Konno-Ichikawa hierarchy

Authors

Zhijun Qiao, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

1-16-1995

Abstract

A finite-dimensional involutive system is presented, and the Wadati-Konno- Ichikawa (WKI) hierarchy of nonlinear evolution equations and their commutator representations are discussed in this article. By this finite-dimensional involutive system, it is proven that under the so-called Bargmann constraint between the potentials and the eigenfunctions, the eigenvalue problem (called the WKI eigenvalue problem) studied by Wadati, Konno, and Ichikawa [J. Phys. Sot. Jpn. 47, 1698 (1979)] is nonlinearized as a completely integrable Hamiltonian system in the Liouville sense. Moreover, the parametric representation of the solution of each equation in the WKI hierarchy is obtained by making use of the solution of two compatible systems.

Comments

© 1995 American Institute of Physics. Original published version available at https://doi.org/10.1063/1.530979

Recommended Citation

Qiao, Zhijun. 1995. “A Completely Integrable System and Parametric Representation of Solutions of the Wadati–Konno–Ichikawa Hierarchy.” Journal of Mathematical Physics 36 (7): 3535–40. https://doi.org/10.1063/1.530979.

First Page

3535

Last Page

3540

Publication Title

Journal of Mathematical Physics

DOI

10.1063/1.530979