Integrability of the Kruskal--Zabusky Discrete Equation by Multiscale Expansion

Journal Article · Mon Mar 08 00:00:00 EST 2010 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3367081· OSTI ID:21371058

Levi, Decio ^[1]; Scimiterna, Christian ^[2]

---

1. Dipartimento di Ingegneria Elettronica, Universita degli Studi Roma Tre and INFN Sezione di Roma III, Via della Vasca Navale 84, 00146 Roma (Italy)
2. Dipartimento di Ingegneria Elettronica, Universita degli Studi Roma Tre, Via della Vasca Navale 84, 00146 Roma (Italy)

In 1965 Kruskal and Zabusky in a very famous article in Physical Review Letters introduced the notion of 'soliton' to describe the interaction of solitary waves solutions of the Korteweg de Vries equation (KdV). To do so they introduced a discrete approximation to the KdV, the Kruskal-Zabusky equation (KZ). Here we analyze the KZ equation using the multiscale expansion and show that the equation is only A{sub 2} integrable.

• OSTI ID: 21371058
• Journal Information: AIP Conference Proceedings, Vol. 1212, Issue 1; Conference: 1. international workshop on nonlinear and modern mathematical physics, Beijing (China), 15-21 Jul 2009; Other Information: DOI: 10.1063/1.3367081; (c) 2010 American Institute of Physics; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
HARMONIC OSCILLATORS
INTEGRAL CALCULUS
INTEGRAL EQUATIONS
KORTEWEG-DE VRIES EQUATION
MATHEMATICAL SOLUTIONS
REVIEWS
SOLITONS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
DOCUMENT TYPES
EQUATIONS
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
QUASI PARTICLES