Self - Similar Solutions for Nonlinear Schrodinger Equations ∗

نویسندگان

  • CHANGXING MIAO
  • BO ZHANG
  • XIAOYI ZHANG
  • C. MIAO
  • B. ZHANG
  • X. ZHANG
چکیده

In this paper we study self-similar solutions for nonlinear Schrödinger equations using a scaling technique and the partly contractive mapping method. We establish the small global well-posedness of the Cauchy problem for nonlinear Schrödinger equations in some non-reflexive Banach spaces which contain many homogeneous functions. This we do by establishing some a priori nonlinear estimates in Besov spaces, employing the mean difference characterization and multiplication in Besov spaces. These new global solutions to nonlinear Schrödinger equations with small data admit a class of self-similar solutions. Our results improve and extend the well-known results of Planchon [18], Cazenave and Weissler [4, 5] and Ribaud and Youssfi [20].

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تاریخ انتشار 2003