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Smoothing properties for the higher-order nonlinear Schrödinger equation with constant coefficients
(Nonlinear Analysis: Theory, Methods & Applications, 2009-08-15) Alves, Margareth; Sepúlveda, Mauricio; Vera, Octavio
We study local and global existence and smoothing properties for the initial value problem associated to a higher-order nonlinear Schrödinger equation with constant coefficients which appears as a model for propagation of pulse in an optical fiber.
Analyticity and smoothing effect for the coupled system of equations of Korteweg-de vries type with a single point singularity
(Acta Applicandae Mathematicae, 2011-01) Alves, Margareth S.; Calsavara, Bianca M. R.; Rivera, Jaime E. Muñoz; Sepúlveda, Mauricio; Villagrán, Octavio Vera
Using Bourgain spaces and the generator of dilation P=3t ∂ t +x ∂ x , which almost commutes with the linear Korteweg-de Vries operator, we show that a solution of the initial value problem associated for the coupled system of equations of Korteweg-de Vries type which appears as a model to describe the strong interaction of weakly nonlinear long waves, has an analyticity in time and a smoothing effect up to real analyticity if the initial data only have a single point singularity at x=0.