On Separation of Variables for Integrable Equations of Soliton Type

Details On Separation of Variables for Integrable Equations of Soliton Type On Separation of Variables for Integrable Equations of Soliton Type

2010-01-03

arxiv.org/abs/1001.0376v1

JNMP, 14 (2007), P. 353-374

Nonlinear Sciences

Exactly Solvable and Integrable Systems

22 pages

Scientific paper

10.2991/jnmp.2007.14.3.5

We propose a general scheme for separation of variables in the integrable Hamiltonian systems on orbits of the loop algebra $\mathfrak{sl}(2,\Complex)\times \mathcal{P}(\lambda,\lambda^{-1})$. In particular, we illustrate the scheme by application to modified Korteweg--de Vries (MKdV), sin(sinh)-Gordon, nonlinear Schr\"odinger, and Heisenberg magnetic equations.

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