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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.