Localized states in the conserved Swift-Hohenberg equation with cubic nonlinearity
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چکیده
منابع مشابه
Localized states in the conserved Swift-Hohenberg equation with cubic nonlinearity.
The conserved Swift-Hohenberg equation with cubic nonlinearity provides the simplest microscopic description of the thermodynamic transition from a fluid state to a crystalline state. The resulting phase field crystal model describes a variety of spatially localized structures, in addition to different spatially extended periodic structures. The location of these structures in the temperature v...
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The cubic-quintic Swift-Hohenberg equation (SH35) provides a convenient order parameter description of several convective systems with reflection symmetry in the layer midplane, including binary fluid convection. We use SH35 with an additional quadratic term to determine the qualitative effects of breaking the midplane reflection symmetry on the properties of spatially localized structures in t...
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Stable spatially localized structures occur in many systems of physical interest. Examples can be found in the fields of optics, chemistry, fluid mechanics, and neuroscience to name a few. The models used to describe these systems have much in common. They are typically of at least fourth order in spatial derivatives, invariant under spatial translations and reflections, and exhibit bistability...
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The Swift-Hohenberg equation with quadratic and cubic nonlinearities exhibits a remarkable wealth of stable spatially localized states. The presence of these states is related to a phenomenon called homoclinic snaking. Numerical computations are used to illustrate the changes in the localized solution as it grows in spatial extent and to determine the stability properties of the resulting state...
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The one-dimensional Swift-Hohenberg equation is known to exhibit a variety of localized states within the so-called pinning or snaking region. Single-pulse states consist of single localized structures within the spatial domain, and are organized into a snakes-and-ladders structure within the pinning region. Multipulse states consist of two or more localized structures within the domain, but th...
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2013
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.87.042915