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A sharp threshold of blow-up for coupled nonlinear Schrödinger equations. (English) Zbl 1189.35312
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)].

35Q55NLS-like (nonlinear Schrödinger) equations
35J60Nonlinear elliptic equations
78A60Lasers, masers, optical bistability, nonlinear optics
35B10Periodic solutions of PDE
35B44Blow-up (PDE)
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