Orbital stability of standing waves for nonlinear fractional Schrödinger equation with unbounded potential
2019 ◽
Vol 12
(03)
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pp. 1950043
Keyword(s):
In this paper, the orbital stability of standing waves for nonlinear fractional Schrödinger equation is considered. By constructing the constrained functional extreme-value problem, the existence of standing waves is studied. With the help of the orbital stability theories presented by Grillakis, Shatah and Strauss, the orbital stability of standing waves is determined by the sign of a discriminant. To our knowledge, it is the first time that the abstract orbital stability theories presented by Grillakis, Shatah and Strauss are applied to study the stability of solutions for fractional evolution equation.
2015 ◽
Vol 29
(3)
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pp. 1017-1030
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2006 ◽
Vol 2006
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pp. 1-7
2018 ◽
Vol 122
(6)
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pp. 64001
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Fourier spectral method with an adaptive time strategy for nonlinear fractional Schrödinger equation
2019 ◽
Vol 36
(4)
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pp. 823-838
2019 ◽
Vol 166
◽
pp. 206-223