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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Orbital stability of periodic traveling-wave solutions for the regularized Schamel equation

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de Andrade, Thiago Pinguello [1] ; Pastor, Ademir [2]
Total Authors: 2
[1] Univ Tecnol Fed Parana, Dept Matemat, Av Alberto Carazzai 1640, BR-86300000 Cornelio Procopio, PR - Brazil
[2] IMECC UNICAMP, Rua Sergio Buarque Holanda 651, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: PHYSICA D-NONLINEAR PHENOMENA; v. 317, p. 43-58, MAR 1 2016.
Web of Science Citations: 5

In this work we study the orbital stability of periodic traveling-wave solutions for dispersive models. The study of traveling waves started in the mid-18th century when John S. Russel established that the flow of water waves in a shallow channel has constant evolution. In recent years, the general strategy to obtain orbital stability consists in proving that the traveling wave in question minimizes a conserved functional restricted to a certain manifold. Although our method can be applied to other models, we deal with the regularized Schamel equation, which contains a fractional nonlinear term. We obtain a smooth curve of periodic traveling-wave solutions depending on the Jacobian elliptic functions and prove that such solutions are orbitally stable in the energy space. In our context, instead of minimizing the augmented Hamiltonian in the natural codimension two manifold, we minimize it in a ``new{''} manifold, which is suitable to our purposes. (C) 2015 Elsevier B.V. All rights reserved. (AU)

FAPESP's process: 13/08050-7 - Nonlinear dispersive evolution equations and applications
Grantee:Ademir Pastor Ferreira
Support type: Regular Research Grants