KAM Tori for the Derivative Quintic Nonlinear Schrodinger Equation

This paper is concerned with one-dimensional derivative quintic nonlinear Schrodinger equation,iut—uxx+i(|u|4u)x=0,x eT.The existence of a large amount of quasi-periodic solutions with two frequencies for this equation is established.The proof is based on partial Birkhoff normal form technique and an unbounded KAM theorem.We mention that in the present paper the mean value of u does not need to be zero,but small enough,which is different from the assumption(1.7)in Geng-Wu[J.Math.Phys.、53,102702(2012)].

This paper is concerned with one-dimensional derivative quintic nonlinear Schr?dinger equation,iut-uxx + i（|u|4 u）x = 0, x ∈ T.The existence of a large amount of quasi-periodic solutions with two frequencies for this equation is established. The proof is based on partial Birkhoff normal form technique and an unbounded KAM theorem. We mention that in the present paper the mean value of u does not need to be zero, but small enough, which is different from the assumption（1.7） in Geng–Wu [J. Math. Phys., 53, 102702（2012）].