Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Global Small Solutions of the Cauchy Problem for Nonisotropic Schrödinger Equations

  • Zhao, Xiangqing (Department of Mathematics, Zhejiang Ocean University) ;
  • Cui, Shangbin (Department of Mathematics, Sun Yat-Sen University)
  • Received : 2006.08.28
  • Published : 2008.03.31
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Abstract

In this paper we study the existence of global small solutions of the Cauchy problem for the non-isotropically perturbed nonlinear Schr$\"{o}$dinger equation: $iu_t\;+\;{\Delta}u\;+\;{\mid}u{\mid}^{\alpha}u\;+\;a{\Sigma}_i^d\;u_{x_ix_ix_ix_i}$ = 0, where a is real constant, 1 $\leq$ d < n is a integer is a positive constant, and x = $(x_1,x_2,\cdots,x_n)\;\in\;R^n$. For some admissible ${\alpha}$ we show the existence of global(almost global) solutions and we calculate the regularity of those solutions.

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