General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences - Tập 468 Số 2142 - Trang 1716-1740 - 2012
Yasuhiro Ohta1, Jianke Yang2
1Department of Mathematics, Kobe University Rokko, Kobe 657-8501, Japan
2Department of Mathematics and Statistics, University of Vermont, Burlington, VT 05401, USA

Tóm tắt

General high-order rogue waves in the nonlinear Schrödinger equation are derived by the bilinear method. These rogue waves are given in terms of determinants whose matrix elements have simple algebraic expressions. It is shown that the general N -th order rogue waves contain N −1 free irreducible complex parameters. In addition, the specific rogue waves obtained by Akhmediev et al. (Akhmediev et al. 2009 Phys. Rev. E 80 , 026601 ( doi:10.1103/PhysRevE.80.026601 )) correspond to special choices of these free parameters, and they have the highest peak amplitudes among all rogue waves of the same order. If other values of these free parameters are taken, however, these general rogue waves can exhibit other solution dynamics such as arrays of fundamental rogue waves arising at different times and spatial positions and forming interesting patterns.

Từ khóa


Tài liệu tham khảo

10.1137/0150021

Akhmediev N., 1985, Generation of a periodic sequence of picosecond pulses in an optical fiber: exact solutions, Sov. Phys. JETP, 89, 1542

10.1007/BF01017105

10.1103/PhysRevE.80.026601

10.1016/j.physleta.2008.12.036

10.1016/j.physleta.2009.04.023

10.1016/j.physleta.2011.05.047

10.1002/sapm1967461133

Bertola M.& Tovbis A.. 2010 Universality for the focusing nonlinear Schrödinger equation at the gradient catastrophe point: rational breathers and poles of the tritronquee solution to Painleve I. See http://arxiv.org/abs/1004.1828.

10.5194/nhess-11-667-2011

10.1140/epjst/e2010-01252-9

10.1088/1751-8113/44/43/435204

10.1063/1.1654836

10.1017/CBO9780511543043

10.1023/A:1016167008456

10.1007/BF01018207

10.2977/prims/1195182017

10.1103/PhysRevE.84.056611

10.1038/nphys1740

10.1111/j.1467-9590.2011.00525.x

10.1017/S0334270000003891

Sato M., 1981, Soliton equations as dynamical systems on a infinite dimensional Grassmann manifolds, RIMS Kokyuroku, 439, 30

10.1038/nature06402

10.1007/BF00913182

Zakharov V. E., 1972, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Sov. Phys. JETP, 34, 62

Thông tin
Thông tin xuất bản

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Tập 468 Số 2142

1716-1740

Thông tin tác giả