A note on the stability and instability of travelling wave of Korteweg

Facultad de Ciencias Naturales y Exactas
Universidad del Valle
A Note on the Stability and Instability of
Travelling Wave of
Korteweg-de Vries Type: The Periodic Case
José R. Quintero
Universidad del Valle
Received: July 1, 2010 Accepted: October 6, 2010
Pág. 57-72
Abstract
In this paper we adapt the work of M. Grillakis, J. Shatah, and W. Strauss, or J. Bona, P.
Souganidis and W. Strauss to the periodic case in spaces having the mean zero property in order
to establish the orbital stability/instability of periodic travelling wave solutions of a generalized
Korteweg-de Vries type equation.
Keywords: KdV type models; periodic travelling waves; orbital stability/instability.
MSC (2000): 35Q53, 35B35, 76B30.
1 Introduction
It is well known, these models describe the unidirectional propagation of
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A note on the stability and instability of travelling wave of Korteweg-de Vries type
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2 Periodic travelling waves of the generalized KdV type model
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A note on the stability and instability of travelling wave of Korteweg-de Vries type
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A note on the stability and instability of travelling wave of Korteweg-de Vries type
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3 Adaptation of Grillakis, Shatah, Strauss Approach
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A note on the stability and instability of travelling wave of Korteweg-de Vries type
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A note on the stability and instability of travelling wave of Korteweg-de Vries type
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A note on the stability and instability of travelling wave of Korteweg-de Vries type
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A note on the stability and instability of travelling wave of Korteweg-de Vries type
References
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Author’s address
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