Ground states for a system of nonlinear Schrodinger equations with three wave interaction

摘要

We consider a system of nonlinear Schroumldinger equations with three wave interaction studying the existence of ground state solutions. In particular, we find a vector ground state, namely, a ground state (u(1),u(2),u(3)) such that u(i)not equal 0 for all i=1,2,3.