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Snaking and isolas of localised states in bistable discrete lattices
homoclinic snaking dissipative soliton coupled cells
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2010/11/10
We consider localised states in a discrete bistable Allen-Cahn equation. This model equation combines bistability and local cell-to-cell coupling in the simplest possible way. The existence of stable ...
On some special solutions to periodic Benjamin-Ono equation with discrete Laplacian
Benjamin-Ono equation nonlocal integrable system Macdonald polynomial integrals of motion
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2010/4/8
We investigate a periodic version of the Benjamin-Ono (BO) equation associated with a discrete Laplacian. We find some special solutions to this equation, and calculate the values of the first two int...
The Discrete and Continuous Painleve VI Hierarchy and the Garnier Systems
Painleve VI Hierarchy the Garnier Systems
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2010/11/2
We present a general scheme to derive higher-order members of the Painleve VI (PVI) hierarchy of ODE's as well as their difference analogues. The derivation is based on a discrete structure that sits...