Abstract
We consider a semilinear elliptic system which includes the model system of the W-strings in the cosmology as a special case. We prove existence of multi-string solutions and obtain precise asymptotic decay estimates near infinity for the solutions. As a special case of this result we solve an open problem posed by Yang [14].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ambjorn J., Olesen P. (1988). Anti-screening of large magnetic fields by vector bosons. Phys. Lett. B 214, 565–569
Baraket S., Pacard F. (1998). Construction of singular limits for a semilinear elliptic equation in dimension 2. Cal. Var. PDE 6, 1–38
Bartolucci D., Tarantello G. (2002). The Liouville equations with singular data and their applications to electroweak vortices. Comm. Math. Phys. 229, 3–47
Chae D., Yu Imanuvilov O. (2000). The existence of non-topological multivortex solutions in the relativistic self-dual Chern–Simons theory. Comm. Math. Phys. 215, 119–142
Chae D., Tarantello G. (2004). On planar selfdual electroweak vortices. Annales IHP Analyse non linéaire. 21(2): 187–207
Chae D., Tarantello G. Selfgravitating electroweak strings. J. Diff. Eqns. (to appear)
Gradshteyn I.S., Ryzhik I.M.: Tables of integrals, series, and products. 6th edn., Academic (2000)
Liouville J. (1853). Sur l’équation aux différences partielles \({d^{2} \log \lambda \over dudv} \pm {\lambda \over 2a^{2}} = 0\). J. Math. Pures Appl. 18: 71–72
Polchinsky J.: Introduction to Cosmic F- and D-Strings. hep-th/0412244 (2004)
Spruck J., Yang Y. (1992). On multivortices in the electroweak theory I: existence of periodic solutions. Comm. Math Phys. 144, 1–16
Spruck J., Yang Y. (1992). On multivortices in the electroweak theory II: existence of bogomol’nyi solutions in \(\mathbb{R}^2\). Comm. Math. Phys. 144, 215–234
Yang Y. (1994). Obstruction to the existence of static cosmic strings in an Abelian-Higgs model. Phys. Rev. Lett. 73, 10–13
Yang Y. (1995). Prescribing topological defects for the coupled Einstein and Abelian Higgs equations Comm. Math. Phys. 170, 541–582
Yang Y. (2001). Solitons in field theory and nonlinear analysis. Springer, Berlin Heidelberg, New York
Zeidler, E.: Nonlinear functional analysis and its applications, Vol. 1. Springer, Berlin Heidelberg, New York (1985)
Author information
Authors and Affiliations
Corresponding author
Additional information
AMS Subject Classifications (2000): 35J45, 35J60, 37K40, 70S15
Rights and permissions
About this article
Cite this article
Chae, D. Existence of Multistring Solutions of the Self-Gravitating Massive W-Boson. Lett Math Phys 73, 123–134 (2005). https://doi.org/10.1007/s11005-005-0003-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11005-005-0003-0