컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0204 |
|---|---|
| 분류(Section) | Special Session |
| 분과(Session) | (SS-07) Understanding of Nonlinear Dispersive Equations (SS-07) |
| 발표시간(Time) | 20th-D-14:00 -- 14:30 |
| 영문제목 (Title(Eng.)) |
Global existence and finite time blow-up for the dispersion-managed NLS |
| 저자(Author(s)) |
Mi-Ran Choi1, Younghun Hong2, Young-Ran Lee1 Sogang University1, Chung-Ang University2 |
| 초록본문(Abstract) | In this talk, we consider the dispersion managed nonlinear Schr\"odinger equation for positive average dispersion \[ i\partial_t u+d_{\text{av}}\partial_x^2u+ \int_0^1 e^{-ir\partial_x^2}\big(|e^{ir\partial_x^2}u|^{p-1}e^{ir\partial_x^2}u\big)dr=0, \] which is a model for strong dispersion management in nonlinear optics. We first construct an extremizer for the Gagliardo-Nirenberg-Strichartz inequality via the concentration compactness method. Using the critical element associated with the Gagliardo-Nirenberg Strichartz inequality, we establish a dichotomy between global existence and finite-time blowup for the mass supercritical cases, $p > 9$. |
| 분류기호 (MSC number(s)) |
35Q55 |
| 키워드(Keyword(s)) | Dispersion management, NLS, global existence, blow-up |
| 강연 형태 (Language of Session (Talk)) |
Korean |