### Abstract

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.

Original language | English |
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Journal | Electronic Journal of Differential Equations |

Volume | 2016 |

Publication status | Published - 2016 Jan 25 |

### Fingerprint

### Keywords

- Analytic smoothing effect
- Global solution
- Non elliptic Schrödinger equation
- Nonlinear Schrödinger equation

### ASJC Scopus subject areas

- Analysis

### Cite this

**Analytic smoothing effect for the cubic hyperbolic schrödinger equation in two space dimensions.** / Hoshino, Gaku; Ozawa, Tohru.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Analytic smoothing effect for the cubic hyperbolic schrödinger equation in two space dimensions

AU - Hoshino, Gaku

AU - Ozawa, Tohru

PY - 2016/1/25

Y1 - 2016/1/25

N2 - 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.

AB - 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.

KW - Analytic smoothing effect

KW - Global solution

KW - Non elliptic Schrödinger equation

KW - Nonlinear Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=84955562979&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84955562979&partnerID=8YFLogxK

M3 - Article

VL - 2016

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

SN - 1072-6691

ER -