Asymptotic behavior of solutions of the Korteweg-de Vries equation for large times

Journal Article · Wed Sep 10 00:00:00 EDT 1986 · J. Sov. Math.; (United States)

DOI:https://doi.org/10.1007/BF01095099· OSTI ID:5661408

Buslaev, V S; Sukhanov, V V

For the KdV equation a complete asymptotic expansion of the dispersive tail for large times is described, and generalized wave operators are introduced. The asymptotics for large times of the spectral Schroedinger equation with a potential of the type of a solution of the KdV equation is studied. It is shown that the KdV equation is connected in a specific manner with the structure of the asymptotics of solutions of the spectral equation. As a corollary, known explicit formulas for the leading terms of the asymptotics of solutions of the KdV equation in terms of spectral data corresponding to the initial conditions are obtained. A plan for justifying the results listed is outlined.

• OSTI ID: 5661408
• Journal Information: J. Sov. Math.; (United States), Vol. 34:5; 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

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