Long-time asymptotic behavior of the solutions of the Korteweg-De Vries equations

Journal Article · Wed May 20 00:00:00 EDT 1987 · J. Sov. Math.; (United States)

OSTI ID:5742187

Buslaev, V S; Sukhanov, V V

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

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