On the orbital stability of traveling waves that behave such as particles
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Abstract
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.
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Eduardo Ibargüen-Mondragón, University of Nariño, Colombia
Doctor in Mathematics Affiliation: University of Nariño. GIBIMMA Research Group, Department of Mathematics and Statistics, University of Nariño, Pasto, Colombia
Mawency Vergel Ortega
Doctor of Education. Affiliation: Francisco de Paula Santander University, Cúcuta, Colombia.
Sandra Hidalgo-Bonilla, Yachay Experimental Technology Research University, Ecuador
Doctor in Chemistry. Affiliation: School of Chemical Sciences and Engineering, Yachay Experimental Technology Research University, Yachay Tech, San Miguel de Urcuquí, Ecuador.