John B. Gonzalez

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math.AP2009

Solutions of the Nonlinear Schrodinger Equation with Prescribed Asymptotics at Infinity

John B. Gonzalez

We prove local existence and uniqueness of solutions for the one-dimensional nonlinear Schrödinger (NLS) equations $i u_{t} + u_{xx} \pm ∣ u ∣^{2} u = 0$ in classes of smooth functions th…

math.AP2009

Unbounded Solutions of the Modified Korteweg-De Vries Equation

John B. Gonzalez

We prove local existence and uniqueness of solutions of the focusing modified Korteweg - de Vries equation $u_{t} + u^{2} u_{x} + u_{xxx} = 0$ in classes of unbounded functions that admit…