A sharp threshold of blow-up for coupled nonlinear Schrodinger equations

This paper is concerned with the coupled supercritical nonlinear Schrodinger 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 Fanelli and Montefusco (2007 J. Phys. A: Math. Theor. 40 14139–50x).