sigma models of nonlinear evolution equations

Journal Article · Sat Mar 15 04:00:00 EST 1980 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.21.1513· OSTI ID:5410722

Orfanidis, S J

A systematic method is developed of constructing the sigma model associated with any given nonlinear evolution equation solvable by the inverse scattering method. The sigma model is obtained from the adjoint representation of the group associated with the Lax representation of the evolution equation. Baecklund transformations for the sigma model and for the evolution equation are realized as gauge transformations. The complete integrability of the sigma model follows from Pohlmeyer's R transformation which is systematically constructed in each case. The examples of the sine-Gordon, nonlinear Schroedinger, Korteweg-- de Vries , and modified Korteweg-- de Vries equations are discussed in detail.

• Research Organization: Department of Electrical Engineering, Rutgers University, Piscataway, New Jersey 08854
• OSTI ID: 5410722
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 21:6; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
DIFFERENTIAL EQUATIONS
EIGENSTATES
EQUATIONS
FIELD EQUATIONS
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
INVERSE SCATTERING PROBLEM
LIE GROUPS
LORENTZ TRANSFORMATIONS
MATHEMATICAL MODELS
PARTICLE MODELS
PARTICLE PROPERTIES
SCHROEDINGER EQUATION
SIGMA MODEL
SINE-GORDON EQUATION
SPACE-TIME
SPIN
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS
TRANSFORMATIONS
WAVE EQUATIONS