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

Autor(es)

de Andrade, Thiago Pinguello ^[1] ; Pastor, Ademir ^[2]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: PHYSICA D-NONLINEAR PHENOMENA; v. 317, p. 43-58, MAR 1 2016.
• Citações Web of Science: 5

Resumo

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)

• Processo FAPESP: 13/08050-7 - Equações de evolução dispersivas não-lineares e aplicações
• Beneficiário: Ademir Pastor Ferreira
• Modalidade de apoio: Auxílio à Pesquisa - Regular