Inverse scattering solution of non-linear evolution equations in one space dimension: an introduction
Journal Article
·
· Hadronic J.; (United States)
OSTI ID:6615096
A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly.
- Research Organization:
- Universidad Complutense, Madrid, Spain
- OSTI ID:
- 6615096
- Journal Information:
- Hadronic J.; (United States), Journal Name: Hadronic J.; (United States) Vol. 2:4; ISSN HAJOD
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
645500 -- High Energy Physics-- Scattering Theory-- (-1987)
658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIFFERENTIAL EQUATIONS
EIGENVALUES
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FIELD EQUATIONS
FUNCTIONS
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MATHEMATICAL OPERATORS
NONLINEAR PROBLEMS
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658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIFFERENTIAL EQUATIONS
EIGENVALUES
EQUATIONS
FIELD EQUATIONS
FUNCTIONS
INVERSE SCATTERING PROBLEM
KORTEWEG-DE VRIES EQUATION
MATHEMATICAL OPERATORS
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
SCHROEDINGER EQUATION
SINE-GORDON EQUATION
TIME DEPENDENCE
WAVE EQUATIONS
WAVE FUNCTIONS