Optical temporal rogue waves in the generalized inhomogeneous nonlinear Schrödinger equation with varying higher-order even and odd terms
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We investigate optical temporal rogue waves of the generalized nonlinear Schrödinger (NLS) equation with higher-order odd and even terms and space- and time-modulated coefficients, which includes the NLS equation, Lakshmanan–Porsezian–Daniel (LPD) equation, Hirota equation, Chen–Lee–Liu equation, and Kaup–Newell derivative NLS equation. Based on the similarity reduction method, the generalized NLS equation can be reduced to the integrable LPD–Hirota equation under a set of constraint conditions, from which the solutions of generalized NLS equation can be obtained in the basis of solutions of the LPD–Hirota equation and the similarity transformation. In particular, the first- and second-order self-similar rogue wave solutions of the generalized NLS equation are derived under different parameters, and the contour profiles and density evolutions of self-similar rogue wave solutions are given to study their wave structures and dynamic properties. At the same time, the motions of the hump and valleys related to the self-similar rogue waves are also given, from which we can control and manage the self-similar rogue waves by adjusting the third-order dispersion term. These results may be useful in nonlinear optics and related fields.
KeywordsThe generalized nonlinear Schrödinger (NLS) equation The LPD–Hirota equation Similarity reduction method Rogue wave solutions Motions of the hump and valleys
The authors would like to thank the referees for their valuable suggestions. This work was supported by the National Natural Science Foundation of China (Nos. 61178091, 11326165), Zhejiang Provincial Natural Science Foundation of China (No. LQ12A01008), and China Postdoctoral Science Foundation (No. 2014M550863).
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