Infinite hierarchy of nonlinear Schrodinger equations and their solutions

被引：150

作者：

Ankiewicz, A. ^{[1
]}

Kedziora, D. J. ^{[1
]}

Chowdury, A. ^{[1
]}

Bandelow, U. ^{[2
]}

Akhmediev, N. ^{[1
]}

机构：

[1] Australian Natl Univ, Res Sch Phys & Engn, Opt Sci Grp, Canberra, ACT 0200, Australia

[2] Weierstrass Inst Appl Anal & Stochast, D-10117 Berlin, Germany

来源：

PHYSICAL REVIEW E | 2016年 / 93卷 / 01期

基金：

澳大利亚研究理事会;

关键词：

HEISENBERG SPIN CHAIN; SOLITON-SOLUTIONS; INTEGRABILITY; EVOLUTION; FIBERS; WAVES;

D O I：

10.1103/PhysRevE.93.012206

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

We study the infinite integrable nonlinear Schrodinger equation hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, Kuznetsov-Ma breathers, periodic solutions, and rogue wave solutions for this infinite-order hierarchy. We find that "even-order" equations in the set affect phase and "stretching factors" in the solutions, while "odd-order" equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are always complex.

引用

页数：10

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