We study the Cauchy problem for the cubic hyperbolic Schrödinger 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.
|Journal||Electronic Journal of Differential Equations|
|Publication status||Published - 2016 Jan 25|
- Analytic smoothing effect
- Global solution
- Non elliptic Schrödinger equation
- Nonlinear Schrödinger equation
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