Open AccessOn the orbital stability of traveling waves that behave such as particles
Author(s) -
Eduardo Ibargüen-Mondragón,
Mawency Vergel Ortega,
Sandra Hidalgo-Bonilla
Publication year - 2021
Publication title -
boletín redipe
Language(s) - English
Resource type - Journals
ISSN - 2256-1536
DOI - 10.36260/rbr.v10i2.1202
Subject(s) - stability (learning theory) , classical mechanics , compressibility , physics , simple (philosophy) , work (physics) , orbital mechanics , mathematics , mathematical analysis , mechanics , computer science , quantum mechanics , philosophy , epistemology , machine learning , satellite , astronomy
Properties that solitary waves share with particles have contributed significantly to the development of new theories and technological advances in different areas of knowledge. In this sense, the study of orbital stability of solitary waves is key in solitary wave dynamics. Although the definition of orbital stability is relatively simple, the mathematical analysis required to verify it is quite complex. However, the theory of Grillakis, Shatah and Strauss provides us with a very useful criterion to verify orbital stability. In this work, we present their theory and apply it to analyse the orbital stability of Generalized Korteweg-de Vries equation, Compressible fluid equation, and one-dimensional Benney-Luke equation. For the first two equations, the criterion guaranteed the orbital stability of the solitary waves. For the third one, it was guaranteed only for certain ranges of its parameters.