The initial-boundary-value problem for the 1D nonlinear Schrödinger equation on the half-line

By Justin Holmer. Differential and Integral Equations, 2005

122 citations recorded by the source corpus.

We prove, by adapting the method of Colliander-Kenig (9), local well- posedness of the initial-boundary value problem for the one-dimensional nonlinear Schrodinger equation i@tu+@ 2 xu+�u|u| � 1 = 0 on the half-line under low boundary regularity assumptions.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1a75a86a2582f1caa5d7e846e17f92fa612fd3a0

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In Mathematical Physics

1. Dionyssios Mantzavinos
2. Gino Biondini

In Statistical and Nonlinear Physics

1. Dionyssios Mantzavinos
2. Gino Biondini
3. Mark J. Ablowitz

Citations in the corpus

• Long‐Time Asymptotics for the Focusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions at Infinity and Asymptotic Stage of Modulational Instability (2015, methodology): “Well-posedness of the NLS equation on the half-line with data in Sobolev spaces was established independently and via different approaches by Holmer [42], Bona, Sun and Zhang [10] and Fokas, Himonas and the second author [33].”