Self-focusing and modulational analysis for nonlinear Schroedinger equations

Thesis/Dissertation · Fri Jan 01 04:00:00 EST 1982

OSTI ID:7094522

Weinsten, M I

For the initial-value problem (IVP) for the nonlinear Schroedinger equation, a sufficient condition for the existence of a unique global solution of the IVP is found. The condition is derived by solving a variational problem to obtain the best constant for a classical interpolation estimate of Nirenberg and Gagliardo. A systematic analysis of the singular structure is presented here for the first time. Methods apply to the general critical case. Linear modulational stability of the ground state relative to small perturbations in NLS and/or the initial data is established in the subcritical case. A sufficient condition for the existence of a unique global solution of a generalized Korteweg-de Vries equation is obtained in terms of the solitary (traveling) wave solution.

• Research Organization: New York Univ., NY (USA)
• OSTI ID: 7094522
• 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
DIFFERENTIAL EQUATIONS
EQUATIONS
KORTEWEG-DE VRIES EQUATION
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
SCHROEDINGER EQUATION
SINGULARITY
STABILITY
VARIATIONAL METHODS
WAVE EQUATIONS