Existence and Orbital Stability of Cnoidal Waves for a 1D Boussinesq Equation
نویسندگان
چکیده
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 fundamental period T0 will be built by using Jacobian elliptic functions. Stability (orbital) of these solutions by periodic disturbances with 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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ورودعنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2007 شماره
صفحات -
تاریخ انتشار 2007