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A lower-bound estimate of injectivity radius for complete Riemannian manifolds is discussed in a pure geometric viewpoint and is applied to study tangent cones at in nity of certain gradient Ricci sol...
Some properties of the correspondence between the non-commutative versions of the (generalized) sine-Gordon (NCGSG$_{1,2}$) and the massive Thirring (NCGMT$_{1,2}$) models are studied. Our method rel...
We elaborate two generic methods for producing two-dimensional (2D) spatial soliton arrays (SSAs) in the framework of the cubic-quintic (CQ) complex Ginzburg-Landau (CGL) model. The first approach de...
We consider a class of nonlinear Schrodinger / Gross-Pitaevskii (NLS/GP) equations with periodic potentials, having an even symmetry. We construct "solitons", centered about any point of symmetry of t...
We consider soliton formation in thermal nonlinear media bounded by rectangular cross-sections and uncover a new class of nonlinear stationary topological state. Specifically, we find that stationary ...

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