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Boussinesq Equations and Other Systems for Small-Amplitude Long Waves in Nonlinear Dispersive Media
In part I of this work (Bona J L, Chen M and Saut J-C 2002 Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media I: Derivation and the linear theory J.…
Local smoothing properties of dispersive equations
Is it possible for time evolution partial differential equations which are reversible and conservative to smooth locally the initial data? For the linear wave equation, for instance, the answer is…
Ill-Posedness Issues for the Benjamin-Ono and Related Equations
We establish that the Cauchy problem for the Benjamin--Ono equation and for a rather general class of nonlinear dispersive equations with dispersion slightly weaker than that of the Korteweg--de…
Solitary waves of generalized Kadomtsev-Petviashvili equations
Boussinesq Equations and Other Systems for Small-Amplitude Long Waves in Nonlinear Dispersive Media. I: Derivation and Linear Theory
In the present script, a four-parameter family of Boussinesq systems are derived from the two-dimensional Euler equations for free-surface flow and criteria are formulated to help decide which of these equations one might choose in a given modeling situation.
Travelling Waves for the Gross-Pitaevskii Equation II
The purpose of this paper is to provide a rigorous mathematical proof of the existence of travelling wave solutions to the Gross-Pitaevskii equation in dimensions two and three. Our arguments, based…
Nonlocal models for nonlinear, dispersive waves
Existence results for the flow of viscoelastic fluids with a differential constitutive law