|
Teoreticheskaya i Matematicheskaya Fizika, 1980, Volume 45, Number 3, Pages 365–376
(Mi tmf4342)
|
|
|
|
This article is cited in 2 scientific papers (total in 2 papers)
Generalization of the model of a relativistic string in a geometrical approach
B. M. Barbashov, V. V. Nesterenko, A. M. Chervyakov
Abstract:
A model of a one-dimensionally extended relativistic object is proposed. Its dynamics is determined by the requirement that its covering surface in Minkowski space have constant mean curvature $h$ with respect to each normal direction. A special case of such surfaces is the world surface of a relativistic string (minimal surface with $h=0$). The methods of differential geometry are used to investigate the most interesting cases when the enveloping pseudo-Euclidean space-time has dimensions $D=3,4$. In the ease $D=3$, the proposed model is described by the single nonlinear equation $\square\varphi=h\sh\varphi$. In fourdimensional
space-time, the dynamics of the model is determined by the system of two
equations
$$
\square\varphi=\frac{1}{2}h(e^\varphi-e^{-\varphi}\cos\theta), \quad
\square\theta=\frac{1}{2}he^{-\varphi}\sin\theta.
$$
A Lax representation for this system is obtained in a geometrical approach, and the use of the inverse scattering technique is briefly discussed.
Received: 06.12.1979
Citation:
B. M. Barbashov, V. V. Nesterenko, A. M. Chervyakov, “Generalization of the model of a relativistic string in a geometrical approach”, TMF, 45:3 (1980), 365–376; Theoret. and Math. Phys., 45:3 (1980), 1082–1089
Linking options:
https://www.mathnet.ru/eng/tmf4342 https://www.mathnet.ru/eng/tmf/v45/i3/p365
|
Statistics & downloads: |
Abstract page: | 299 | Full-text PDF : | 123 | References: | 50 | First page: | 2 |
|