×

zbMATH — the first resource for mathematics

On stabilization of solutions of complex coupled nonlinear Schrödinger equations. (English) Zbl 1070.81043
The complex coupled nonlinear Schrödinger (CCNLS) equations have been studied from a practical and a theoretical point of view. The authors study the chaos control of periodic and quasi-periodic solutions of both focusing and defocusing of integrable and nonintegrable CCNLS equations. It was shown that the nonsymmetric CCNLS equation has only quasi-periodic solutions. Both periodic and quasi-periodic solutions of CCNLS equations are not chaotic solutions since Lyapunov exponents approach zero and these solutions do not display sensitive dependence on initial conditions.

MSC:
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)
37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1142/S0129183101002073 · doi:10.1142/S0129183101002073
[2] DOI: 10.1016/S0167-2789(00)00021-X · Zbl 0971.37035 · doi:10.1016/S0167-2789(00)00021-X
[3] DOI: 10.1016/0167-2789(94)00186-T · Zbl 0900.35368 · doi:10.1016/0167-2789(94)00186-T
[4] Wright O. C., Physica D 126 pp 175–
[5] Yew A. C., Indiana Univ. Math. J. 49 pp 1079–
[6] DOI: 10.1006/jdeq.2000.3922 · Zbl 1021.34036 · doi:10.1006/jdeq.2000.3922
[7] DOI: 10.1103/PhysRevE.61.5886 · doi:10.1103/PhysRevE.61.5886
[8] DOI: 10.1103/PhysRevE.60.1019 · doi:10.1103/PhysRevE.60.1019
[9] DOI: 10.1103/PhysRevLett.86.5043 · doi:10.1103/PhysRevLett.86.5043
[10] DOI: 10.1364/OL.16.000018 · doi:10.1364/OL.16.000018
[11] DOI: 10.1103/PhysRevLett.64.1196 · Zbl 0964.37501 · doi:10.1103/PhysRevLett.64.1196
[12] DOI: 10.1016/0375-9601(92)90745-8 · doi:10.1016/0375-9601(92)90745-8
[13] DOI: 10.1016/0167-2789(95)00276-6 · Zbl 0925.93366 · doi:10.1016/0167-2789(95)00276-6
[14] Ramirez J., IEEE Trans. Circuits Syst. 2 pp 168–
[15] DOI: 10.1016/S0378-4371(00)00590-2 · Zbl 0972.37054 · doi:10.1016/S0378-4371(00)00590-2
[16] Mahmoud G. M., Il Nuovo Cimento B 116 pp 1113–
[17] Mahmoud G. M., Int. J. Bifur. Chaos
[18] DOI: 10.1016/S0960-0779(02)00411-3 · Zbl 1098.70527 · doi:10.1016/S0960-0779(02)00411-3
[19] DOI: 10.1016/0167-2789(85)90011-9 · Zbl 0585.58037 · doi:10.1016/0167-2789(85)90011-9
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.