Nonlinear Waves on Localized and Periodic Backgrounds with Time-Space Modulation

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Communications in Theoretical Physics ›› 2017, Vol. 67 ›› Issue (05) : 520-526.

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Nonlinear Waves on Localized and Periodic Backgrounds with Time-Space Modulation

Mei-Kun Liu^1,2, Zhan-Ying Yang^1,2, Wen-Li Yang^2,3

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Abstract

We present one family of general analytical solutions for the generalized nonlinear Schrödinger equation with time-space modulation via the method of a combination of the Darboux transformation and similarity transformation. Nonlinear waves on different localized and periodic backgrounds depending on the corresponding nonlinearity modulations are obtained. In particular, we demonstrate the existence and property of localized modes on a double-periodic background under a special designed optical lattice potential. Our results may raise the possibility of related experiments and potential applications in nonlinear optics and Bose-Einstein condensates.

Key words

rogue waves / breathers / localized and periodic background / time-space modulation

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Mei-Kun Liu, Zhan-Ying Yang, Wen-Li Yang. Nonlinear Waves on Localized and Periodic Backgrounds with Time-Space Modulation[J]. Communications in Theoretical Physics, 2017, 67(05): 520-526

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