School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Document Type


Publication Date



In this article, a system of finite-dimensional involutive functions is presented and proven to be integrable in the Liouville sense. By using the nonlinearization method, the C. Neumann system associated with the modified Korteweg-de Vries (mKdV) hierarchy is obtained. Thus, the C. Neumann system is shown to be completely integrable via a gauge transformation between it and an integrable Hamiltonian system. Finally, the solution of a stationary mKdV equation and the involutive solutions of the mKdV hierarchy are secured. As two examples, the involutive solutions are given for the mKdV equation: u,+ ;uXXX- $u2u,=0 and the 5th mKdV equation v,- ~v,,,~~+~u~v,,~+~vv,v,,+ &~-$v4uX=0.


©1994, American Institute of Physics.

First Page


Last Page


Publication Title

Journal of Mathematical Physics



Included in

Mathematics Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.