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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Official URL: http://www.springerlink.com/content/h676217u54175t...

Related URL: http://dx.doi.org/10.1007/BF00382623

## Abstract

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 |
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Source: | Copyright of this article belongs to Springer-Verlag. |

ID Code: | 19606 |

Deposited On: | 22 Nov 2010 12:19 |

Last Modified: | 08 Jun 2011 07:32 |

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