Qualitative analysis of the eigenvalue problem for two coupled Ginzburg-Landau equations
100 24
Keywords:
Ginzburg-Landau equations, eigenvalue problem, qualitative analysisAbstract
Eigenvalue problem for two coupled Ginzburg-Landau equations is numerically investigated. The fixed points of corresponding equations system are found. The classification of these points is made. It is shown that the investigated equations set has local minima, global minima, local maximum, and the points refer to saddle points. The phase portraits of corresponding ordinary differential equations and the dependence of some parameters of the equations system and the total energy on the initial values are given.The profiles of dimensionless energy density of the equations set for the different initial values of are given. The dependence of the parameters of the system m1, m2 and the total energy M on the initial values of c0 is investigated.
References
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4. Bezerra de Mello E.R., Brihaye Y. and Hartmann B. Strings in de Sitter space // Phys. Rev.D. – 2003. – Vol. 67. – P. 124008 [arXiv:hep-th/0302212].
5. Bazeia D. and Gomes A.R. Bloch Brane // JHEP. – 2004. – Vol. 0405. – P. 012 (13p.). [arXiv:hep-th/0403141].
6. Vernov S.Y. Construction of Exact Solutions in Two-Fields Models and the Crossing of the Cosmological Constant Barrier // Teor. Mat. Fiz. – 2008. – Vol.155. – P. 47. [Theor. Math. Phys. 155, 544 (2008)] [arXiv:astro-ph/0612487].
7. Cordero R. and Mota R.D. Soliton Stability in a Generalized Sine-Gordon Potential // Int. J. Theor. Phys. – 2004. – Vol. 43. – P. 2215-2222. [arXiv:0709.2822 [hep-th]].
8. Aref'eva I.Y., Bulatov N.V. and Vernov S.Y. Stable Exact Solutions in Cosmological Models with Two Scalar Fields // Theor. Math. Phys. – 2010. – Vol. 163. – P. 788-803.[arXiv:0911.5105 [hep-th]].
9. Dzhunushaliev V., Myrzakulov K. and Myrzakulov R. Boson stars from a gauge condensate // Mod. Phys. Lett. A. – 2007. – Vol.22. – P. 273-282. [arXiv:gr-qc/0604110].
10. Dzhunushaliev V., Folomeev V., Myrzakulov K. and Myrzakulov R.Cosmic string with two interacting scalar fields // Mod. Phys. Lett. A. – 2007. – Vol. 22. – P.407-414 [arXiv:gr-qc/0610111].
11. Dzhunushaliev V. and Folomeev V. 4D static solutions with interacting phantom fields // Int. J. Mod. Phys. D. – 2008. – Vol. 17. – P. 2125-2142. [arXiv:0711.2840 [gr-qc]].
12. Dzhunushaliev V., Folomeev V., Myrzakulov K. and Myrzakulov R. Phantom fields: bounce solutions in the early Universe and S-branes // Int. J. Mod. Phys. D. – 2008.– Vol. 17. – P. 2351-2358. [arXiv:gr-qc/0608025].
13. Folomeev V. Bianchi type I model with two interacting scalar fields // Int. J. Mod. Phys. D. – 2007. – Vol. 16. – P. 1845-1852. [arXiv:gr-qc/0703004].
14. Dzhunushaliev V. Thick brane solution in the presence of two interacting scalar fields // Grav. Cosmol. – 2007. – Vol. 13. – P. 302-307. [arXiv:gr-qc/0603020].
15. Dzhunushaliev V., Folomeev V., Singleton D. and Aguilar-Rudametkin S. 6D thick branes from interacting scalar fields // Phys. Rev. D. – 2008. – Vol. 77. – P. 044006 [arXiv:hep-th/0703043].
16. Dzhunushaliev V., Folomeev V., Myrzakulov K. and Myrzakulov R. Thick brane in 7D and 8D spacetimes // Gen. Rel. Grav. – 2009. – Vol. 41. – P. 131-146. [arXiv:0705.4014 [gr-qc]].
17. Dzhunushaliev V., Folomeev V. and Minamitsuji M. Thick de Sitter brane solutions in higher dimensions // Phys. Rev. D. – 2009. – Vol. 79. – P. 024001 [arXiv:0809.4076 [gr-qc]].
18. Dzhunushaliev V.Two interacting GL-equations in High-Tc superconductivity and quantum chromodynamics // arXiv:0705.3170 [cond-mat.supr-con].
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Dzhunushaliev, V., Folomeev, V., Myrzakulov, R., & Urazalina, A. (2015). Qualitative analysis of the eigenvalue problem for two coupled Ginzburg-Landau equations. Recent Contributions to Physics (Rec.Contr.Phys.), 52(1), 68–76. Retrieved from https://bph.kaznu.kz/index.php/zhuzhu/article/view/963
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Theoretical Physics. Nuclear and Elementary Particle Physics. Astrophysics
