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

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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 languageEnglish
Pages (from-to)1093-1105
Number of pages13
JournalDiscrete and Continuous Dynamical Systems
Volume27
Issue number3
DOIs
Publication statusPublished - Jul 2010
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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