Stationary phase theory and passage through resonance

Journal of Mathematical Analysis and Applications

Volumn 205, Issue 1, 1997, Pages 186-196

  Skinner, L A ^a  

^a UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; FOURIER TRANSFORMS; FUNCTIONS; INTEGRAL EQUATIONS; LAPLACE TRANSFORMS; NUMERICAL ANALYSIS;

ASYMPTOTIC EXPANSION; FORCED HARMONIC OSCILLATOR; FOURIER INTEGRALS; LAPLACE INTEGRALS; PASSAGE THROUGH RESONANCE; STATIONARY PHASE THEORY;

MATHEMATICAL TECHNIQUES;

EID: 0030609321     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1996.5179     Document Type: Article

References (10)

1. Ablowitz M. J., Funk B., Newell A. C. Semi-resonant interactions and frequency dividers. Stud. Appl. Math. 52:1973;51-74.
2. Bleistein N. Uniform asymptotic expansion of integrals with stationary point rear algebraic singularity. Comm. Pure Appl. Math. 19:1966;353-370.
3. Bleistein N., Handelsman R. A. Asymptotic Expansions of Integrals. 1975;Holt, Rinehart & Winston, New York.
4. Bosely D. L., Kevorkian J. Adiabatic invariance and transient resonance in very slowly varying oscillatory Hamiltonian systems. SIAM J. Appl. Math. 52:1992;494-527.
5. Erdelyi A. Asymptotic Expansions. 1956;Dover, New York.
6. Gautesen A. K. Resonance for a forced N-dimensional oscillator. SIAM J. Appl. Math. 27:1974;526-530.
7. Kevorkian J. Passage through resonance for a one-dimensional oscillator with slowly varying frequency. SIAM J. Appl. Math. 20:1971;364-373.
8. Kevorkian J., Cole J. D. Perturbation Methods in Applied Mathematics. 1981;Springer-Verlag, Berlin/New York.
9. Sanders J. A., Verhulst F. Averaging Methods in Nonlinear Dynamical Systems. 1985;Springer-Verlag, New York.
10. Skinner L. A. Matched asymptotic expansions of integrals. IMA J. Appl. Math. 50:1993;77-90.