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Darboux transformations and rogue wave solutions of a generalized AB system for the geophysical flows

机译:地球物理流动广义AB系统的DARBOUX变换和流浪波解

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In this paper, we investigate a generalized AB system, which is used to describe certain baroclinic instability processes in the geophysical flows. For the two short waves and mean flow, we derive out the Darboux and generalized Darboux transformations, both relevant to the coefficient of the nonlinear term and coefficient related to the shear. When the coefficient of the nonlinear term is positive, with the generalized Darboux transformation, we present the algorithm to derive the Nth-order (N = 1,2, . . .) rogue wave solutions. The first- and second-order rogue wave solutions are shown, where our first-order rogue waves are different from those in the existing literatures. The two short waves and mean flow are related to the coefficient of the nonlinear term under certain conditions; the coefficient related to the shear has a linear effect on the mean flow while has no effect on the two short waves. The Nth-order rogue wave solutions turn to be singular when the coefficient of the nonlinear term is negative. (C) 2018 Elsevier Ltd. All rights reserved.
机译:在本文中,我们研究了广泛的AB系统,其用于描述地球物理流动中的某些曲金稳定性过程。对于两个短波和平均流动,我们源于与剪切相关的非线性术语和系数的系数相关的Darboux和广义的Darboux转换。当非线性术语的系数是阳性的,随着广义的DARBOUX转换,我们介绍了算法导出NTH阶(n = 1,2,...)流氓波解决方案。示出了第一和二阶流氓波解决方案,其中我们的一阶流氓波与现有文献中的一阶流氓波不同。两个短波和平均流动与某些条件下的非线性术语的系数有关;与剪切有关的系数对平均流量具有线性效应,同时对两个短波没有影响。当非线性术语的系数为阴性时,nth阶流氓波解决方案转向单数。 (c)2018年elestvier有限公司保留所有权利。

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