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Type: Artigo de periódico
Author: Pava, JA
Abstract: This work is concerned with nonlinear stability properties of periodic travelling wave solutions of the Hirota-Satsuma system {u(t) + u(xxx) + 6u(x)u = 2bvv(x) v(t) + v(xxx) + 3uv(x) = 0 posed in R with b > 0. We prove that this system is globally well posed in L-per(2)([0, L]) x H-per(1) ([0, L]) by using Bourgain's space framework. Also shown is the existence of at least two nontrivial smooth curves of periodic travelling wave solutions depending on the classical Jacobian elliptic functions. We find dnoidal and cnoidal waves solutions. Then we prove the nonlinear stability of the dnoidal waves solutions in the energy space L-per(2)([0, L]) x H-per(1) ([0, L]). The Floquet theory is used to obtain a detailed spectral analysis of the Jacobian form of Lame's equation which is required in our stability theory.
Country: EUA
Editor: Khayyam Publ Co Inc
Citation: Differential And Integral Equations. Khayyam Publ Co Inc, v. 18, n. 6, n. 611, n. 645, 2005.
Rights: fechado
Date Issue: 2005
Appears in Collections:Unicamp - Artigos e Outros Documentos

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