Analytic method for finding stationary solutions to generalized nonlinear Schrödinger equations

被引：5

作者：

Qiang, Y. Long ^{[1
]}

Broderick, Neil G. R. ^{[2
,3
]}

de Sterke, C. Martijn ^{[1
]}

机构：

[1] Univ Sydney, Inst Photon & Opt Sci IPOS, Sch Phys, Sydney, NSW 2006, Australia

[2] Univ Auckland, Dept Phys, Private Bag 92019, Auckland 1142, New Zealand

[3] Univ Auckland, Dodd Walls Ctr Photon & Quantum Technol, Private Bag 92019, Auckland 1142, New Zealand

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2024年 / 462卷

基金：

澳大利亚研究理事会;

关键词：

Solitons; Analytic method; Systematic; General; Nonlinear Waves; Exponential convergence; SOLITARY WAVE SOLUTIONS; EVOLUTION; SOLITONS; PULSES;

D O I：

10.1016/j.physd.2024.134148

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a method to generate analytic, stationary solutions to generalized nonlinear Schr & ouml;dinger equations with complicated dispersion profiles. The experimental observation of such solutions in a fiber laser was recently reported. Our method proceeds in a systematic fashion and does not require initial guesses. The solutions take the form of an exponentially converging sum of functions, each with an infinite number of discontinuous derivatives at the origin, which disappear upon summation. They can be found conveniently using a symbolic manipulation program. Our method can not only find stable solitons, but also higher order solutions that tend to be unstable and that are difficult to find numerically.

引用

页数：6

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