Domains of existence and asymptotics of complex periodic solutions of the stationary nonlinear Schroedinger equation

Journal Article · Thu Feb 28 04:00:00 EST 2008 · Quantum Electronics (Woodbury, N.Y.)

DOI:https://doi.org/10.1070/QE2008V038N02ABEH013591; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21185830

Kuratov, A S; Petnikova, V M; Shuvalov, V V ^[1]

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1. International Laser Center, M. V. Lomonosov Moscow State University, Moscow (Russian Federation)

The domains of existence for complex periodic particular solutions of the stationary nonlinear Schroedinger equation are determined. It is shown that, if the solution of this class has at least one point in which the amplitude does not have a local extremum and is equal to zero, then the phase of the solution is constant. The asymptotics of such solutions are considered and a simple procedure (the replacement of one set of the 'basis' elliptic functions by another) is described which allows one to construct the solution corresponding to the nonlinearity of one type (defocusing or focusing) from the known solution for the nonlinearity of another type (focusing or defocusing). (nonlinear optical phenomena)

• OSTI ID: 21185830
• Journal Information: Quantum Electronics (Woodbury, N.Y.), Journal Name: Quantum Electronics (Woodbury, N.Y.) Journal Issue: 2 Vol. 38; ISSN 1063-7818
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
ASYMPTOTIC SOLUTIONS
NONLINEAR PROBLEMS
PERIODICITY
SCHROEDINGER EQUATION