(Non)linear instability of periodic traveling waves: Klein-Gordon and KdV type equations

Autor(es)

Pava, Jaime Angulo ^[1] ; Natali, Fabio ^[2]

Afiliação do(s) autor(es)

^[1] IME USP, Dept Math, BR-05508090 Sao Paulo - Brazil

^[2] DMA UEM, Dept Math, BR-87020900 Maringa, Parana - Brazil

• Tipo de documento: Artigo Científico
• Fonte: ADVANCES IN NONLINEAR ANALYSIS; v. 3, n. 2, p. 95-123, MAY 2014.
• Citações Web of Science: 6

Resumo

We prove the existence and nonlinear instability of periodic traveling wave solutions for the critical one-dimensional Klein-Gordon equation. We also establish a linear instability criterium for a KdV type system. An application of this approach is made to obtain the linear/nonlinear instability of vector cnoidal wave profiles. Finally, via a theoretical and numerical approach we show the linear stability or instability of periodic positive and sign changing waves, respectively, for the critical Korteweg-de Vries equation. (AU)

• Processo FAPESP: 12/50521-4 - Equações dispersivas não-lineares: estabilidade (instabilidade) não-linear para ondas viajantes de tipo periódico
• Beneficiário: Jaime Angulo Pava
• Modalidade de apoio: Auxílio à Pesquisa - Regular