Abstract
With the help of the similarity transformation connected the variable-coefficient nonlinear Schrödinger equation with the standard nonlinear Schrödinger equation, we firstly obtain first-order and second-order rogue wave solutions in two dimensional graded-index waveguides. Then, we investigate the nonlinear tunneling of controllable rogue waves when they pass through nonlinear barrier and nonlinear well. Our results indicate that the propagation behaviors of rogue waves, such as postpone, sustainment and restraint, can be manipulated by choosing the relation between the maximum value of the effective propagation distance Z m and the effective propagation distance corresponding to maximum amplitude of rogue waves Z 0. Postponed, sustained and restrained rogue waves can tunnel through the nonlinear barrier or well with increasing, unchanged and decreasing amplitudes by modulating the ratio of the amplitudes of rogue waves to barrier or well height.
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This work was supported by the Applied nonlinear Science and Technology from the most important among all the top priority disciplines of Zhejiang Province.
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Zhu, HP. Nonlinear tunneling for controllable rogue waves in two dimensional graded-index waveguides. Nonlinear Dyn 72, 873–882 (2013). https://doi.org/10.1007/s11071-013-0759-1
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DOI: https://doi.org/10.1007/s11071-013-0759-1