Global Small Solutions of the Cauchy Problem for NonisotropicSchodinger Equations
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In this paper we study the existence of global small solutions of the Cauchy problem for the non-isotropically perturbed nonlinear Schr¨odinger equation: iut + △u + |u|^ u + a ∑^d _i uxixixixi = 0, where a is real constant, 1 ≤ d < n is a integer, is a positive constant, and x = (x1, x2, · · · , xn) ∈ Rⁿ. For some admissible α we show the existence of global(almost global) solutions and we calculate the regularity of those solutions.
Abstract
In this paper we study the existence of global small solutions of the Cauchy problem for the non-isotropically perturbed nonlinear Schr¨odinger equation: iut + △u + |u|^ u + a ∑^d _i uxixixixi = 0, where a is real constant, 1 ≤ d < n is a integer, is a positive constant, and x = (x1, x2, · · · , xn) ∈ Rⁿ. For some admissible α we show the existence of global(almost global) solutions and we calculate the regularity of those solutions.
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