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Dedicated to Jean-Claude Saut, who gave me water to cross the desert. Abstract For a large class of nonlinear Schrödinger equations with nonzero conditions at infinity and for any speed c less than the sound velocity, we prove the existence of finite energy traveling waves moving with speed c in any space dimension N ≥ 3. Our results are valid as well for… (More)

We are interested in the existence of travelling-wave solutions to a system which modelizes the motion of an uncharged impurity in a Bose condensate. We prove that in space dimension one, there exist travelling-waves moving with velocity c if and only if c is less than the sound velocity at infinity. In this case we investigate the structure of the set of… (More)

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