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We study the nonlinear Schrödinger equation (NLS) with bounded initial data which does not vanish at infinity. Examples include periodic, quasi-periodic and random initial data. On the lattice we prove… Click to show full abstract
We study the nonlinear Schrödinger equation (NLS) with bounded initial data which does not vanish at infinity. Examples include periodic, quasi-periodic and random initial data. On the lattice we prove that solutions are polynomially bounded in time for any bounded data. In the continuum, local existence is proved for real analytic data by a Newton iteration scheme. Global existence for NLS with a regularized nonlinearity follows by analyzing a local energy norm.
Keywords:
schr dinger;
bounded initial;
nonlinear schr;
dinger equation;
initial data
Journal Title: Journal of Statistical Physics
Year Published: 2020
Link to full text (if available)
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Journal Title: Journal of Statistical Physics
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!