Existence and Orbital Stability of Cnoidal Waves for a 1D Boussinesq Equation | Zendy

Jaime Angulo Pava | Zendy; José R. Quintero | Zendy

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Existence and Orbital Stability of Cnoidal Waves for a 1D Boussinesq Equation

Author(s) -

Jaime Angulo Pava,

José R. Quintero

Publication year - 2007

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2007/52020

Subject(s) - algorithm , computer science

We will study the existence and stability of periodic travelling-wave solutions of the nonlinear one-dimensional Boussinesq-type equation Φtt−Φxx+aΦxxxx−bΦxxtt+ΦtΦxx+2ΦxΦxt=0. Periodic travelling-wave solutions with an arbitrary fundamentalperiod T0 will be built by using Jacobian elliptic functions.Stability (orbital) of these solutions by periodic disturbanceswith period T0 will be a consequence of the general stability criteria given by M. Grillakis, J. Shatah, and W. Strauss. A complete study of the periodic eigenvalue problem associated to the Lame equation is set up

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