Numerical study of fractional nonlinear Schrödinger equations
2014 ◽
Vol 470
(2172)
◽
pp. 20140364
◽
Keyword(s):
Blow Up
◽
Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation.
2019 ◽
Vol 42
(18)
◽
pp. 6896-6905
2015 ◽
Vol 258
(3)
◽
pp. 717-735
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2018 ◽
Vol 17
(5)
◽
pp. 1785-1804
◽
2020 ◽
Vol 17
(4)
◽
pp. 329-360
2008 ◽
Vol 153
(4)
◽
pp. 525-539
◽
2015 ◽
Vol 471
(2179)
◽
pp. 20140932
◽
Keyword(s):
2010 ◽
Vol 28
(4)
◽
pp. 1505-1554
◽
Keyword(s):