Focusing singularity of the nonlinear Schroedinger equation

Thesis/Dissertation · Wed Jan 01 04:00:00 EST 1986

OSTI ID:6980172

LeMesurier, B J

A novel adaptive method for computation of cylindrically symmetric singular solutions to the nonlinear Schroedinger equation is introduced. This method is based on a dynamic approximation of the conjectured asymptotic similarity scaling behavior of such solutions and solves for a time dependent rescaling of the solution that develops no singularity. With a cubic nonlinearity, amplitude scaling factors of about 10/sup 10/ were attained on a 356 point spatial grid. This compares with a previous best reported factor of 1400 on a slightly larger grid. The method is also applied to a saturated version of the cubic potential in two dimensions, giving results on the oscillatory behavior that develops there for smaller degrees of saturation and further into the oscillatory stage than earlier studies. It continues to be useful numerically after the initial growth phase, and the main conclusion is that an initial decay of the oscillation amplitude is not sustained at its early rate if at all.

• Research Organization: New York Univ., NY (USA)
• OSTI ID: 6980172
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
ASYMPTOTIC SOLUTIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
POTENTIALS
SCALING LAWS
SCHROEDINGER EQUATION
SINGULARITY
SYMMETRY
WAVE EQUATIONS