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Zbl 1189.35312
Li, Xiaoguang; Wu, Yonghong; Lai, Shaoyong
A sharp threshold of blow-up for coupled nonlinear Schrödinger equations. (English)
[J] J. Phys. A, Math. Theor. 43, No. 16, Article ID 165205, 11 p. (2010). ISSN 1751-8113; ISSN 1751-8121/e

Summary: This paper is concerned with the coupled supercritical nonlinear Schrödinger equations which have applications in many physical problems, especially in nonlinear optics. Two types of new invariant evolution flows are established. A sharp threshold of blow-up and global existence of solutions for the equations is derived. It is shown that the main result obtained includes parts of those presented by {\it L. Fanelli} and {\it E. Montefusco} [J. Phys. A, Math. Theor. 40, No.~47, 14139--14150 (2007; Zbl 1134.35099)].

MSC 2000:: *35Q55 NLS-like (nonlinear Schroedinger) equations
35J60 Nonlinear elliptic equations
78A60 Lasers, etc.
35B10 Periodic solutions of PDE
35B44

Keywords: nonlinear optics; nonlinear Schrödinger equations; Gagliardo-Nirenberg inequality

Citations: Zbl 1134.35099

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