Rogue periodic waves of the focusing nonlinear Schrodinger equation

被引:119
|
作者
Chen, Jinbing [1 ]
Pelinovsky, Dmitry E. [2 ,3 ]
机构
[1] Southeast Univ, Sch Math, Nanjing 210096, Jiangsu, Peoples R China
[2] McMaster Univ, Dept Math, Hamilton, ON L8S 4K1, Canada
[3] Nizhnii Novgorod State Tech Univ, Dept Appl Math, 24 Minin St, Nizhnii Novgorod 603950, Russia
基金
中国国家自然科学基金;
关键词
nonlinear Schrodinger equation; rogue waves; modulational instability of periodic waves; Zakharov-Shabat spectral problem; MODULATIONAL INSTABILITY; INTEGRABLE TURBULENCE; NLS; STABILITY; SOLITONS;
D O I
10.1098/rspa.2017.0814
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrodinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn. Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov-Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine's breather). The magnification factor of the rogue periodic waves is computed as a function of the elliptic modulus. Rogue periodic waves constructed here are compared with the rogue wave patterns obtained numerically in recent publications.
引用
收藏
页数:18
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