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Blow-up solutions of inhomogeneous nonlinear Schrödinger equations

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Abstract

In this paper, we study blow-up solutions to the Cauchy problem of the inhomogeneous nonlinear Schrödinger equation

$$ \partial_t u = i ( f(x) \Delta u + \nabla f(x) \cdot \nabla u +k(x)|u|^2u) $$

on \({\mathbb{R}}^2\). We present existence and non-existence results and investigate qualitative properties of the solutions when they exist.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 2 Science Drive 2, 117543, Republic of Singapore

    Peter Y. H. Pang

  2. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People's Republic of China

    Hongyan Tang

  3. Institute of Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100080, People's Republic of China

    Youde Wang

Authors
  1. Peter Y. H. Pang
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  2. Hongyan Tang
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  3. Youde Wang
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Corresponding author

Correspondence to Peter Y. H. Pang.

Additional information

Mathematics Subject Classification (2000) 35Q55, 35G25

Dedicated respectfully to Professor Weiyue Ding on the occasion of his sixtieth birthday.

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Pang, P.Y.H., Tang, H. & Wang, Y. Blow-up solutions of inhomogeneous nonlinear Schrödinger equations. Calc. Var. 26, 137–169 (2006). https://doi.org/10.1007/s00526-005-0362-5

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