Variational approximations to homoclinic snaking in continuous and discrete systems.
نویسندگان
چکیده
Localized structures appear in a wide variety of systems, arising from a pinning mechanism due to the presence of a small-scale pattern or an imposed grid. When there is a separation of length scales, the width of the pinning region is exponentially small and beyond the reach of standard asymptotic methods. We show how this behavior can be obtained using a variational method, for two systems. In the case of the quadratic-cubic Swift-Hohenberg equation, this gives results that are in agreement with recent work using exponential asymptotics. In addition, the method is applied to a discrete system with cubic-quintic nonlinearity, giving results that agree well with numerical simulations.
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عنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 84 6 Pt 2 شماره
صفحات -
تاریخ انتشار 2011