INITIAL-BOUNDARY-VALUE PROBLEM FOR THE RELATIVISTIC STRING WITH MASSIVE ENDS

Citation
Bm. Barbashov et Gs. Sharov, INITIAL-BOUNDARY-VALUE PROBLEM FOR THE RELATIVISTIC STRING WITH MASSIVE ENDS, Theoretical and mathematical physics, 101(2), 1994, pp. 1332-1345
Citations number
7
Categorie Soggetti
Mathematical Method, Physical Science",Physics,"Physycs, Mathematical
ISSN journal
00405779
Volume
101
Issue
2
Year of publication
1994
Pages
1332 - 1345
Database
ISI
SICI code
0040-5779(1994)101:2<1332:IPFTRS>2.0.ZU;2-S
Abstract
It is shown that the initial-boundary-value problem for a relativistic string with masses at the ends can be solved for the most general for m of specification of the initial position and initial velocities of t he points of the string. An investigation is made of the connection be tween the freedom in the parametrization of the initial curve and the reparametrization invariance preserving linearity of the equations of motion of the string. The posed problem is solved by extending the sol ution determined by the initial conditions from the restricted initial region to the entire world surface of the string by means of boundary conditions of various types: the mass at a given end is equal to zero , is infinitely large, or is finite. In the last case it is shown that the problem of the extension reduces to the solution of a normal syst em of ordinary differential equations. Specific examples are considere d.