Electron. J. Diff. Equ., Vol. 2016 (2016), No. 34, pp. 1-8.

Analytic smoothing effect for the cubic hyperbolic Schrodinger equation in two space dimensions

Gaku Hoshino, Tohru Ozawa

Abstract:
We study the Cauchy problem for the cubic hyperbolic Schrodinger equation in two space dimensions. We prove existence of analytic global solutions for sufficiently small and exponential decaying data. The method of proof depends on the generalized Leibniz rule for the generator of pseudo-conformal transform acting on pseudo-conformally invariant nonlinearity.

Submitted April 4, 2015. Published January 25, 2016.
Math Subject Classifications: 35Q55.
Key Words: Nonlinear Schrodinger equation; non elliptic Schrodinger equation; analytic smoothing effect; global solution.

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Gaku Hoshino
Department of Applied Physics
Waseda University
Tokyo 169-8555, Japan
email: gaku-hoshino@ruri.waseda.jp
Tohru Ozawa
Department of Applied Physics
Waseda University
Tokyo 169-8555, Japan
email: txozawa@waseda.jp

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