Finite speed of disturbance for the nonlinear Schrödinger equation
2018 ◽
Vol 149
(6)
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pp. 1405-1419
Keyword(s):
AbstractWe consider the Cauchy problem for the nonlinear Schrödinger equation on the whole space. After introducing a weaker concept of finite speed of propagation, we show that the concatenation of initial data gives rise to solutions whose time of existence increases as one translates one of the initial data. Moreover, we show that, given global decaying solutions with initial data u0, v0, if |y| is large, then the concatenated initial data u0 + v0(· − y) gives rise to globally decaying solutions.
2021 ◽
Vol 382
(1)
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pp. 87-121
2020 ◽
Vol 489
(2)
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pp. 124188
2014 ◽
Vol 98
(1)
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pp. 78-103
2006 ◽
Vol 16
(5)
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pp. 435-481
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