Instability of Double-Periodic Waves in the Nonlinear Schrödinger Equation
It is shown how to compute the instability rates for the double-periodic solutions to the cubic NLS (nonlinear Schrödinger) equation by using the Lax linear equations. The wave function modulus of the double-periodic solutions is periodic both in space and time coordinates; such solutions generalize...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2021-02-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2021.599146/full |
| Summary: | It is shown how to compute the instability rates for the double-periodic solutions to the cubic NLS (nonlinear Schrödinger) equation by using the Lax linear equations. The wave function modulus of the double-periodic solutions is periodic both in space and time coordinates; such solutions generalize the standing waves which have the time-independent and space-periodic wave function modulus. Similar to other waves in the NLS equation, the double-periodic solutions are spectrally unstable and this instability is related to the bands of the Lax spectrum outside the imaginary axis. A simple numerical method is used to compute the unstable spectrum and to compare the instability rates of the double-periodic solutions with those of the standing periodic waves. |
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| ISSN: | 2296-424X |