Solvability of the Cauchy problem of non-isotropic Schrödinger equations in Sobolev spaces

Abstract: We study the existence of solutions for the Cauchy problem of the non-isotropically perturbed nonlinear Schrödinger equation , where , are not simultaneously vanishing real constants, is a positive constant, and . By using Kato’s method, we establish some local existence results for initial data belonging to , where if either , , or , , , if , , and if , , . Global existence is also established under some additional conditions. [Copyright &y& Elsevier]