Dynamics of solitons in the model of nonlinear Schroedinger equation with an external harmonic potential: II. Dark Solitons

Journal Article · Mon Oct 31 00:00:00 EST 2005 · Quantum Electronics (Woodbury, N.Y.)

DOI:https://doi.org/10.1070/QE2005V035N10ABEH003442· OSTI ID:21470822

Hernandez Tenorio, C; Villagran Vargas, E; Serkin, Vladimir N; Aguero Granados, M; Belyaeva, T L; Pena Moreno, R; Morales Lara, L ^[1]

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1. Benemerita Universidad Autonoma de Puebla (Mexico)

The dynamics of dark solitons is studied within the framework of the mathematical model of nonlinear Schroedinger equation (NSE) with an external harmonic potential. A comparative analysis of the solutions of nonstationary problems is performed for a linear harmonic oscillator and the NSE model with a harmonic potential for different signs of the self-action potential. It is shown that the main specific feature of the dynamics of dark NSE solitons in a parabolic trap is the formation of solitons with dynamically changing form factors producing the periodic variation in the modulation depth (the degree of 'blackness') of dark solitons. The oscillation period of the dark soliton does not coincide with the oscillation period of a linear quantum-mechanical oscillator, which is caused by the periodic transformation of the black soliton to the grey one and vice versa. The conditions of applicability of the method of inverse scattering problem are presented, the generalised Lax pair is found, and exact soliton solutions are given for the mathematical NSE model with an external harmonic potential. (solitons)

• OSTI ID: 21470822
• Journal Information: Quantum Electronics (Woodbury, N.Y.), Vol. 35, Issue 10; Other Information: DOI: 10.1070/QE2005v035n10ABEH003442; ISSN 1063-7818
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
FORM FACTORS
HARMONIC OSCILLATORS
HARMONIC POTENTIAL
INVERSE SCATTERING PROBLEM
MATHEMATICAL MODELS
MATHEMATICAL SOLUTIONS
MODULATION
NONLINEAR PROBLEMS
OSCILLATIONS
PERIODICITY
QUANTUM MECHANICS
SCHROEDINGER EQUATION
SOLITONS
TRANSFORMATIONS
DIFFERENTIAL EQUATIONS
DIMENSIONLESS NUMBERS
EQUATIONS
MECHANICS
NUCLEAR POTENTIAL
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
POTENTIALS
QUASI PARTICLES
VARIATIONS
WAVE EQUATIONS