Advances in Differential Equations

Stability of integrable and nonintegrable structures

Claudio Muñoz

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Abstract

In this paper, we give a comprehensive account of several recent results on the stability of nontrivial soliton structures for some well-known non periodic dispersive models. We will focus on the simpler case of the generalized Korteweg-de Vries equations, covering the classical stability results by Bona, Souganidis, and Strauss until the results by Martel and Merle and our recent collaborations with Miguel Alejo and Luis Vega.

Article information

Source
Adv. Differential Equations Volume 19, Number 9/10 (2014), 947-996.

Dates
First available in Project Euclid: 1 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.ade/1404230129

Mathematical Reviews number (MathSciNet)
MR3261918

Zentralblatt MATH identifier
1298.35165

Subjects
Primary: 35Q51: Soliton-like equations [See also 37K40] 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 37K10: Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.) 37K40: Soliton theory, asymptotic behavior of solutions

Citation

Muñoz, Claudio. Stability of integrable and nonintegrable structures. Adv. Differential Equations 19 (2014), no. 9/10, 947--996. https://projecteuclid.org/euclid.ade/1404230129.


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