### Abstract

We investigate existence and asymptotic completeness of the wave operators for nonlinear Schrödinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on the value of the conserved Hamiltonian, below which the exponential potential energy is dominated by the kinetic energy via a Trudinger-Moser type inequality. We prove that if the Hamiltonian is below the critical value, then the solution approaches a free Schrödinger solution at the time infinity.

Original language | English (US) |
---|---|

Pages (from-to) | 1843-1849 |

Number of pages | 7 |

Journal | Nonlinearity |

Volume | 25 |

Issue number | 6 |

DOIs | |

State | Published - Jun 2012 |

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### ASJC Scopus subject areas

- Applied Mathematics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Nonlinearity*,

*25*(6), 1843-1849. https://doi.org/10.1088/0951-7715/25/6/1843

**Scattering for the two-dimensional NLS with exponential nonlinearity.** / Ibrahim, S.; Majdoub, M.; Masmoudi, N.; Nakanishi, K.

Research output: Contribution to journal › Article

*Nonlinearity*, vol. 25, no. 6, pp. 1843-1849. https://doi.org/10.1088/0951-7715/25/6/1843

}

TY - JOUR

T1 - Scattering for the two-dimensional NLS with exponential nonlinearity

AU - Ibrahim, S.

AU - Majdoub, M.

AU - Masmoudi, N.

AU - Nakanishi, K.

PY - 2012/6

Y1 - 2012/6

N2 - We investigate existence and asymptotic completeness of the wave operators for nonlinear Schrödinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on the value of the conserved Hamiltonian, below which the exponential potential energy is dominated by the kinetic energy via a Trudinger-Moser type inequality. We prove that if the Hamiltonian is below the critical value, then the solution approaches a free Schrödinger solution at the time infinity.

AB - We investigate existence and asymptotic completeness of the wave operators for nonlinear Schrödinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on the value of the conserved Hamiltonian, below which the exponential potential energy is dominated by the kinetic energy via a Trudinger-Moser type inequality. We prove that if the Hamiltonian is below the critical value, then the solution approaches a free Schrödinger solution at the time infinity.

UR - http://www.scopus.com/inward/record.url?scp=84861567164&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861567164&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/25/6/1843

DO - 10.1088/0951-7715/25/6/1843

M3 - Article

VL - 25

SP - 1843

EP - 1849

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 6

ER -