Solutions of the Nonlinear Schrödinger Equation with Prescribed Asymptotics at Infinity
نویسنده
چکیده
We prove local existence and uniqueness of solutions for the one-dimensional nonlinear Schrödinger (NLS) equations iut + uxx ± |u| 2 u = 0 in classes of smooth functions that admit an asymptotic expansion at infinity in decreasing powers of x. We show that an asymptotic solution differs from a genuine solution by a Schwartz class function which solves a generalized version of the NLS equation. The latter equation is solved by discretization methods. The proofs closely follow previous work done by the author and others on the Korteweg-De Vries (KdV) equation and the modified KdV equations.
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