Asymptotic behavior of solutions of the Korteweg-de Vries equation

Journal Article · Mon Sep 01 04:00:00 EDT 1986 · J. Okla. State Med. Assoc.; (United States)

OSTI ID:6939958

Buslaev, V S

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 Schrodinger 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: 6939958
• Journal Information: J. Okla. State Med. Assoc.; (United States), Journal Name: J. Okla. State Med. Assoc.; (United States) Vol. 34:5; ISSN JOSMA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ASYMPTOTIC SOLUTIONS
CAUCHY PROBLEM
CONSERVATION LAWS
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
FOURIER TRANSFORMATION
INTEGRAL TRANSFORMATIONS
KORTEWEG-DE VRIES EQUATION
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
QUASI PARTICLES
SCATTERING
SCHROEDINGER EQUATION
SOLITONS
TRANSFORMATIONS
WAVE EQUATIONS