Motion of strings, embedding problem and soliton equations

Lakshmanan, M. ; Tamizhmani, K. M. (1981) Motion of strings, embedding problem and soliton equations Applied Scientific Research, 37 (1-2). pp. 127-143. ISSN 0003-6994

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The motion of a flexible string of constant length in E 3 in interaction, corresponding to a variety of physical situations, is considered. It is pointed out that such a system could be studied in terms of the embedding problem in differential geometry, either as a moving helical space curve in E 3 or by the embedding equations of two dimensional surfaces in E 3. The resulting integrability equations are identifiable with standard soliton equations such as the non-linear Schrodinger, modified K-dV, sine-Gordon, Lund-Regge equations, etc. On appropriate reductions the embedding equations in conjunction with suitable local space-time and/or gauge symmetries reproduce the AKNS-type eigenvalue equations and Riccati equations associated with soliton equations. The group theoretical properties follow naturally from these studies. Thus the above procedure gives a simple geometric interpretation to a large class of the soliton possessing nonlinear evolution equations and at the same time solves the underlying string equations.

Item Type:Article
Source:Copyright of this article belongs to Springer-Verlag.
ID Code:19606
Deposited On:22 Nov 2010 12:19
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