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 give a simple proof of the fact that for a large class of quasilinear elliptic equations and systems the solutions that minimize the corresponding energy in the set of all solutions are radially symmetric. We require just continuous nonlinearities and no cooperative conditions for systems. Thus, in particular, our results cannot be obtained by using the… (More)
We investigate the properties of finite energy travelling waves to the nonlinear Schrödinger equation with nonzero conditions at infinity for a wide class of nonlinearities. In space dimension two and three we prove that travelling waves converge in the transonic limit (up to rescaling) to ground states of the Kadomtsev-Petviashvili equation. Our results… (More)
We consider a two-dimensional generalization of the Benjamin-Ono equation and prove that it admits solitary-wave solutions that are analytic functions. We find the optimal decay rate at infinity of these solitary waves.
Dedicated to Dorel Mihet¸, for his teaching, his friendship, and the inspiration he gave to me. Abstract For a large class of variational problems we prove that minimizers are symmetric whenever they are C 1 .
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)
was not programmed, but they were erased using ultraviolet light while connecting all circuit terminals to ground. A scheme for rail-to-rail continuous-time input signal swing using MIFGTs has been proposed. This scheme provides constant g m. Single-ended and fully differential op-amp architectures based on this scheme and with a novel class-AB output stage… (More)