Comment on connections between nonlinear evolution equations

Journal Article · Sun Nov 15 04:00:00 EST 1981 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.24.2769· OSTI ID:5943339

Fuchssteiner, B; Hefter, E F

An open problem raised in a recent paper by Chodos is treated. We explain the reason for the interrelation between the conservation laws of the Korteweg-de Vries (KdV) and sine-Gordon equations. We point out that it is due to a corresponding connection between the infinite-dimensional Abelian symmetry groups of these equations. While it has been known for a long time that a Baecklund transformation (in this case the Miura transformation) connects corresponding members of the KdV and the sine-Gordon families, it is quite obvious that no Baecklund transformation can exist between different members of these families. And since the KdV and sine-Gordon equations do not correspond to each other, one cannot expect a Baecklund transformation between them; nevertheless we can give explicit relations between their two-soliton solutions. No inverse scattering techniques are used in this paper.

• Research Organization: Fachbereich Mathematik, Universitaet Paderborn, D-4790 Paderborn, Germany
• OSTI ID: 5943339
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 24:10; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CONSERVATION LAWS
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD EQUATIONS
KORTEWEG-DE VRIES EQUATION
LIE GROUPS
MANY-BODY PROBLEM
PARTIAL DIFFERENTIAL EQUATIONS
QUASI PARTICLES
SINE-GORDON EQUATION
SOLITONS
SYMMETRY GROUPS
TWO-BODY PROBLEM