A new classical integrable system associated with the mKdV equation
Department of Mathematics and Physics, Shijiazhuang Tiedao University, 050043, Shijiazhuang, China
* e-mail: Lwei_1981@126.com
Revised: 6 December 2011
Accepted: 6 December 2011
Published online: 23 January 2012
In this paper, a new completely integrable system related to the spectral problem −φ xx + vφ x = λφ and the constrained flows of the mKdV equations are generated. According to the viewpoint of Hamiltonian mechanics, and based on the Euler-Lagrange equations and the Legendre transformations, a reasonable Jacobi-Ostrogradsky coordinate system and the Hamilton equations are obtained. Moreover, by means of the constrained condition between the potential function and the eigenfunction, the involutive solutions of the mKdV equations are given.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2012