ON A WEAK SOLUTION OF THE MIXED NONLINEAR SCHRODINGER-EQUATIONS

In this paper we discuss the mixed nonlinear Schrodinger Equation U(t) =ialphaU(xx)+betaU2UBAR(x)+gamma\Absolute value of U\2U(x)+ig(Absolute value of U 2)U, U(x, 0) = U0(x), () where alpha, beta, gamma are rea l constants with alpha not-equal 0. If the real function g(s) is-an-el ement-of C2(R +) satisfies some conditions, and the initial data U0(x) is-an-element-of H-1(R) are such that the norm parallel-to U0 paralle l-to 2(R) is sufficiently small, then there is a unique weak solution U(x, t) of () such that U(x, t) is-an-element-of C(w)(R; H-1(R)). (C) 1994 Academic Press, Inc.