Concentration of blow-up solutions for the coupled Schrödinger equations in R2R2

We prove a concentration result for blow-up solutions of the coupled Schrödinger equations with non-spherically symmetric initial data in H1(R2)H1(R2). Using the profile decomposition technique and assuming a conjecture of Sirakov is valid, which was proved by Wei and Yao and Ikoma for some cases, we could remove the radial restriction on the initial data and improve the concentration rate from Lü and Liu (2011) [9].