Long-time asymptotic behavior of the solutions of the Korteweg-De Vries equations
Journal Article
·
· J. Sov. Math.; (United States)
OSTI ID:5742187
The complete asymptotic expansion of the dispersion tail in the long-time limit is described for the KdV equation and generalized wave operators are introduced. The long-time asymptotic behavior of the Schroedinger spectral equation is studied assuming a potential of the type of the KdV solution. It is shown that the KdV equation is specifically related with the asymptotic structure of the solutions of the spectral equation. As a corollary, they derive the well-known explicit formulas for the leading asymptotic terms of the KdV solutions in terms of the spectral values corresponding to the initial conditions. A sketch of a proof for the various results is suggested.
- OSTI ID:
- 5742187
- Journal Information:
- J. Sov. Math.; (United States), Vol. 37:4; Other Information: Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR; 120: 32-50(1982)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
KORTEWEG-DE VRIES EQUATION
ASYMPTOTIC SOLUTIONS
SCHROEDINGER EQUATION
CAUCHY PROBLEM
EIGENVALUES
FOURIER TRANSFORMATION
POTENTIALS
QUANTUM MECHANICS
RECURSION RELATIONS
RESONANCE
SCATTERING
SERIES EXPANSION
SPACE-TIME
WAVE FUNCTIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
INTEGRAL TRANSFORMATIONS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
TRANSFORMATIONS
WAVE EQUATIONS
645201* - High Energy Physics- Particle Interactions & Properties-Theoretical- General & Scattering Theory
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
KORTEWEG-DE VRIES EQUATION
ASYMPTOTIC SOLUTIONS
SCHROEDINGER EQUATION
CAUCHY PROBLEM
EIGENVALUES
FOURIER TRANSFORMATION
POTENTIALS
QUANTUM MECHANICS
RECURSION RELATIONS
RESONANCE
SCATTERING
SERIES EXPANSION
SPACE-TIME
WAVE FUNCTIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
INTEGRAL TRANSFORMATIONS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
TRANSFORMATIONS
WAVE EQUATIONS
645201* - High Energy Physics- Particle Interactions & Properties-Theoretical- General & Scattering Theory
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics