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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.

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
Full Text: DOI
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