Infinitely many synchronized solutions to a nonlinearly coupled Schrödinger equations with non-symmetric potentials

. We study a nonlinearly coupled Schr¨odinger equations in R N (2 ≤ N < 6) . Assume that the potentials in the system are continuous functions satisfying some suitable decay assumptions but without any symmetric properties, and the parameters in the system satisfy some restrictions. Applying the Liapunov-Schmidt reduction methods twice and combining localized energy method, we prove that the problem has infinitely many positive synchronized solutions.