Diffractive interaction for short pulses in 2 × 2 system

This paper studies the asymptotic behavior of the diffractive interaction of pulses with two linear phases of length ε << 1 in 2 × 2 semilinear strictly hyperbolic system with constant coefficients. By a formal analysis, it derives problems of profiles in the expansion of the pulse like solution with respect to the length ε, and obtains that the leading profile satisfies a nonlinear Schrodinger type system. The problems of profiles are solved, and the formal expansion is justified. It is observed that there is interaction between two phases starting at the third order profiles.