On the nonlinear stability of mKdV breathers

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Standard

On the nonlinear stability of mKdV breathers. / Alejo Plana, Miguel Angel; Muñoz, Claudio.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 45, No. 43, 430001, 2012.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Alejo Plana, MA & Muñoz, C 2012, 'On the nonlinear stability of mKdV breathers', Journal of Physics A: Mathematical and Theoretical, vol. 45, no. 43, 430001. https://doi.org/10.1088/1751-8113/45/43/432001

APA

Alejo Plana, M. A., & Muñoz, C. (2012). On the nonlinear stability of mKdV breathers. Journal of Physics A: Mathematical and Theoretical, 45(43), [430001]. https://doi.org/10.1088/1751-8113/45/43/432001

Vancouver

Alejo Plana MA, Muñoz C. On the nonlinear stability of mKdV breathers. Journal of Physics A: Mathematical and Theoretical. 2012;45(43). 430001. https://doi.org/10.1088/1751-8113/45/43/432001

Author

Alejo Plana, Miguel Angel ; Muñoz, Claudio. / On the nonlinear stability of mKdV breathers. In: Journal of Physics A: Mathematical and Theoretical. 2012 ; Vol. 45, No. 43.

Bibtex

@article{3ae6fbb971fa4768ac4186d5d0922934,
title = "On the nonlinear stability of mKdV breathers",
abstract = "Breather modes of the mKdV equation on the real line are known to be elastic under collisions with other breathers and solitons. This fact indicates very strong stability properties of breathers. In this communication we describe a rigorous, mathematical proof of the stability of breathers under a class of small perturbations. Our proof involves the existence of a nonlinear equation satisfied by all breather profiles, and a new Lyapunov functional which controls the dynamics of small perturbations and instability modes. In order to construct such a functional, we work in a subspace of the energy one. However, our proof introduces new ideas in order to attack the corresponding stability problem in the energy space. Some remarks about the sine-Gordon case are also considered.",
author = "{Alejo Plana}, {Miguel Angel} and Claudio Mu{\~n}oz",
year = "2012",
doi = "10.1088/1751-8113/45/43/432001",
language = "English",
volume = "45",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "Institute of Physics Publishing Ltd",
number = "43",

}

RIS

TY - JOUR

T1 - On the nonlinear stability of mKdV breathers

AU - Alejo Plana, Miguel Angel

AU - Muñoz, Claudio

PY - 2012

Y1 - 2012

N2 - Breather modes of the mKdV equation on the real line are known to be elastic under collisions with other breathers and solitons. This fact indicates very strong stability properties of breathers. In this communication we describe a rigorous, mathematical proof of the stability of breathers under a class of small perturbations. Our proof involves the existence of a nonlinear equation satisfied by all breather profiles, and a new Lyapunov functional which controls the dynamics of small perturbations and instability modes. In order to construct such a functional, we work in a subspace of the energy one. However, our proof introduces new ideas in order to attack the corresponding stability problem in the energy space. Some remarks about the sine-Gordon case are also considered.

AB - Breather modes of the mKdV equation on the real line are known to be elastic under collisions with other breathers and solitons. This fact indicates very strong stability properties of breathers. In this communication we describe a rigorous, mathematical proof of the stability of breathers under a class of small perturbations. Our proof involves the existence of a nonlinear equation satisfied by all breather profiles, and a new Lyapunov functional which controls the dynamics of small perturbations and instability modes. In order to construct such a functional, we work in a subspace of the energy one. However, our proof introduces new ideas in order to attack the corresponding stability problem in the energy space. Some remarks about the sine-Gordon case are also considered.

U2 - 10.1088/1751-8113/45/43/432001

DO - 10.1088/1751-8113/45/43/432001

M3 - Journal article

VL - 45

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 43

M1 - 430001

ER -

ID: 49604340