Asymptotic solutions of weakly nonlinear, dispersive wave-propagation problems by Fourier analysis
Thesis/Dissertation
·
OSTI ID:5022338
A perturbation method based on Fourier analysis and multiple scales is introduced for solving weakly nonlinear, dispersive wave propagation problems with Fourier transformable initial conditions. Asymptotic solutions are derived for the weakly nonlinear cubic Schroedinger (NLS) equation with variable coefficients and the weakly nonlinear Kortewegde-Vries (KdV) equation; the results for the NLS equation are verified by comparison with numerical solutions. In the special case of constant coefficients, the asymptotic solution for the weakly nonlinear NLS equation agrees to leading order with previously derived results in the literature; in general, this is not true to higher orders. Therefore previous asymptotic results for the strongly nonlinear Schroedinger equation can be valid only for restricted initial conditions. Similar conclusions apply to the KdV equation.
- Research Organization:
- Washington Univ., Seattle, WA (United States)
- OSTI ID:
- 5022338
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
COMPARATIVE EVALUATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
EVALUATION
FOURIER ANALYSIS
KORTEWEG-DE VRIES EQUATION
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
SCHROEDINGER EQUATION
TESTING
VALIDATION
WAVE EQUATIONS
WAVE PROPAGATION
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
COMPARATIVE EVALUATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
EVALUATION
FOURIER ANALYSIS
KORTEWEG-DE VRIES EQUATION
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
SCHROEDINGER EQUATION
TESTING
VALIDATION
WAVE EQUATIONS
WAVE PROPAGATION