Nonlinear Schrödinger equations in inhomogeneous media: wellposedness and illposedness of the Cauchy problem

Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006 ◽

10.4171/022-3/8 ◽

2009 ◽

pp. 156-182

Author(s):

Patrick Gérard

Keyword(s):

Cauchy Problem ◽

Inhomogeneous Media ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem

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On the Cauchy problem for the nonlinear Schrödinger equations with time-dependent linear loss/gain

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2014.03.019 ◽

2014 ◽

Vol 416 (2) ◽

pp. 901-923 ◽

Cited By ~ 13

Author(s):

Binhua Feng ◽

Dun Zhao ◽

Chunyou Sun

Keyword(s):

Cauchy Problem ◽

Nonlinear Schrödinger Equations ◽

Time Dependent ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem ◽

Linear Loss

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The Cauchy problem for non-autonomous nonlinear Schrödinger equations

Science in China Series A Mathematics ◽

10.1360/04ys0012 ◽

2005 ◽

Vol 48 (4) ◽

pp. 522 ◽

Cited By ~ 4

Author(s):

Y. H. Pang Peter

Keyword(s):

Cauchy Problem ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem

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Sharp weights in the Cauchy problem for nonlinear Schrödinger equations with potential

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/s00033-015-0501-6 ◽

2015 ◽

Vol 66 (4) ◽

pp. 2087-2094 ◽

Cited By ~ 5

Author(s):

Rémi Carles

Keyword(s):

Cauchy Problem ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem

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On the Cauchy problem of fourth-order nonlinear Schrödinger equations

Nonlinear Analysis ◽

10.1016/j.na.2006.04.020 ◽

2007 ◽

Vol 66 (12) ◽

pp. 2911-2930 ◽

Cited By ~ 1

Author(s):

Ai Guo ◽

Shangbin Cui

Keyword(s):

Cauchy Problem ◽

Fourth Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem

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Nonexistence of Global Solutions to the Cauchy Problem for the Damped Nonlinear Schrödinger Equations

SIAM Journal on Mathematical Analysis ◽

10.1137/0515028 ◽

1984 ◽

Vol 15 (2) ◽

pp. 357-366 ◽

Cited By ~ 53

Author(s):

Masayoshi Tsutsumi

Keyword(s):

Cauchy Problem ◽

Global Solutions ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem

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The Cauchy problem for nonlinear Schrödinger equations in modulation spaces

Nonlinear Analysis Real World Applications ◽

10.1016/j.nonrwa.2015.01.005 ◽

2015 ◽

Vol 24 ◽

pp. 83-97 ◽

Cited By ~ 2

Author(s):

Shaolei Ru ◽

Jiecheng Chen

Keyword(s):

Cauchy Problem ◽

Nonlinear Schrödinger Equations ◽

Modulation Spaces ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem

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On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations

Journal of Mathematical Physics ◽

10.1063/1.523491 ◽

1977 ◽

Vol 18 (9) ◽

pp. 1794-1797 ◽

Cited By ~ 406

Author(s):

R. T. Glassey

Keyword(s):

Cauchy Problem ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Blowing Up ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem

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The Cauchy Problem of the Nonlinear Schrödinger Equations in ℝ1+1

Acta Mathematicae Applicatae Sinica English Series ◽

10.1007/s10255-007-0398 ◽

2007 ◽

Vol 23 (4) ◽

pp. 593-610

Author(s):

Gui-xiang Xu

Keyword(s):

Cauchy Problem ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem

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The Cauchy Problem for Defocusing Nonlinear Schrödinger Equations with Non-Vanishing Initial Data at Infinity

Communications in Partial Differential Equations ◽

10.1080/03605300802031614 ◽

2008 ◽

Vol 33 (5) ◽

pp. 729-771 ◽

Cited By ~ 22

Author(s):

Clément Gallo

Keyword(s):

Cauchy Problem ◽

Initial Data ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem

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On the well-posedness of the Cauchy problem for some nonlocal nonlinear Schrödinger equations

Nonlinearity ◽

10.1088/1361-6544/aa6aad ◽

2017 ◽

Vol 30 (6) ◽

pp. 2308-2333 ◽

Cited By ~ 1

Author(s):

John Albert ◽

Estapraq Kahlil

Keyword(s):

Cauchy Problem ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem ◽

Nonlocal Nonlinear

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