Soliton surfaces associated with symmetries of ODEs written in Lax representation

Details Soliton surfaces associated with symmetries of ODEs written in Lax representation Soliton surfaces associated with symmetries of ODEs written in Lax representation

2011-11-17

arxiv.org/abs/1111.4161v1

Physics

Mathematical Physics

14 Pages, 2 figures Conference Proceedings for QST7 Prague

Scientific paper

The main aim of this paper is to discuss recent results on the adaptation of the Fokas-Gel'fand procedure for constructing soliton surfaces in Lie algebras, which was originally derived for PDEs [Grundland, Post 2011], to the case of integrable ODEs admitting Lax representations. We give explicit forms of the $\g$-valued immersion functions based on conformal symmetries involving the spectral parameter, a gauge transformation of the wave function and generalized symmetries of the linear spectral problem. The procedure is applied to a symmetry reduction of the static $\phi^4$-field equations leading to the Jacobian elliptic equation. As examples, we obtain diverse types of surfaces for different choices of Jacobian elliptic functions for a range of values of parameters.

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