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Showing 1 to 3 of 3 for “"Dispersive partial differential equations"”.
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The role of smoothing effect in some dispersive equations
… effect in the local well-posedness theory of dispersive partial differential equations in three different contexts. First, we use it to overcome a loss of derivatives in a family of nonlocal dispersive equations. Second, we exploit a discrete version of the smoothing effect to study a discrete …
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Existence and Stability of Solitary Waves for NLS with Defects
… the existence and stability of solitary waves to dispersive partial differential equations and, in particular to nonlinear Schr\"odinger equations with defects nonlinearity. First we identify necessary and sufficient conditions for the existence of appropriately localized waves for the …
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Smoothing properties of certain dispersive nonlinear partial differential equations
… concerned with the smoothing properties of dispersive equations and systems. Smoothing in this context means that the nonlinear part of the solution flow is of higher regularity than the initial data. We establish this property, and some of its consequences, for several equations. The first …