We study the asymptotic behavior of solutions to the Cauchy problem for the higher-order anisotropic nonlinear Schrödinger equation in two space dimensions. We will show the modified scattering for solutions. We continue to develop the factorization techniques, which were started in the papers of N. Hayashi and P. I. Naumkin [Z. Angew. Math. Phys. 59(6), 1002-1028 (2008); J. Math. Phys. 56(9), 093502 (2015)], N. Hayashi and T. Ozawa [Ann. I.H.P.: Phys. Theor. 48, 17-37 (1988)], and T. Ozawa [Commun. Math. Phys. 139(3), 479-493 (1991)]. The crucial point of our approach presented here is the L2-boundedness of the pseudodifferential operators.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics