Well-posedness and existence of standing waves for the fourth order nonlinear Schrödinger type equation

Jun Ichi Segata

doi:10.3934/dcds.2010.27.1093

Well-posedness and existence of standing waves for the fourth order nonlinear Schrödinger type equation

Jun Ichi Segata

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

We consider the fourth order nonlinear Schrödinger type equation (4NLS). The first purpose is to revisit the well-posedness theory of (4NLS). In [8], [9], [20] and [21], they proved the time-local well-posedness of (4NLS) in H⁸(R) with s > 1/2 by using the Fourier restriction method. In this paper we give another proof of above result by using simpler approach than the Fourier restriction method. The second purpose is to construct the exact standing wave solution to (4NLS).

Original language	English
Pages (from-to)	1093-1105
Number of pages	13
Journal	Discrete and Continuous Dynamical Systems
Volume	27
Issue number	3
DOIs	https://doi.org/10.3934/dcds.2010.27.1093
Publication status	Published - Jul 2010
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcds.2010.27.1093

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Well-posedness and existence of standing waves for the fourth order nonlinear Schrödinger type equation

Abstract

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