期刊
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
卷 54, 期 11, 页码 3920-3931出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10773-014-2422-0
关键词
Coupled nonlinear Schrodinger equations; Manakov model; Parity-time symmetry; Global existence
资金
- Ministry of Education and Science of Russian Federation [2014/133]
- FCT (Portugal) [PEst-OE/FIS/UI0618/2014, PTDC/FIS-OPT/1918/2012]
We study a system of two coupled nonlinear Schrodinger equations, where one equation includes gain and the other one includes losses. Strengths of the gain and the loss are equal, i.e., the resulting system is parity-time () symmetric. The model includes both linear and nonlinear couplings, such that when all nonlinear coefficients are equal, the system represents the -generalization of the Manakov model. In the one-dimensional case, we prove the existence of a global solution to the Cauchy problem in energy space H (1), such that the H (1)-norm of the global solution may grow in time. In the Manakov case, we show analytically that the L (2)-norm of the global solution is bounded for all times and numerically that the H (1)-norm is also bounded. In the two-dimensional case, we obtain a constraint on the L (2)-norm of the initial data that ensures the existence of a global solution in the energy space H-1.
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