Reduction of dispersionless coupled Korteweg-de Vries equations to the Euler-Darboux equation

Authors
Citation
Y. Matsuno, Reduction of dispersionless coupled Korteweg-de Vries equations to the Euler-Darboux equation, J MATH PHYS, 42(4), 2001, pp. 1744-1760
Citations number
27
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics
Journal title
JOURNAL OF MATHEMATICAL PHYSICS
ISSN journal
0022-2488 → ACNP
Volume
42
Issue
4
Year of publication
2001
Pages
1744 - 1760
Database
ISI
SICI code
0022-2488(200104)42:4<1744:RODCKV>2.0.ZU;2-M
Abstract
A quasilinear hyperbolic system of two first-order equations is introduced. The system is linearized by means of the hodograph transformation combined with Riemann's method of characteristics. In the process of linearization, the main step is to explicitly express the characteristic velocities in te rms of the Riemann invariants. The procedure is shown to be performed by qu adrature only for specific combinations of the parameters in the system. We then apply the method developed here to the dispersionless versions of the typical coupled Korteweg-de Vries (cKdV) equations including the Broer-Kau p, Ito, Hirota-Satsuma, and Bogoyavlenskii equations and show that these eq uations are transformed into the classical Euler-Darboux equation. A more g eneral quasilinear system of equations is also considered with application to the dispersionless cKdV equations for the Jaulent-Miodek and Nutku-Oguz equations. (C) 2001 American Institute of Physics.