Exact solutions of the Hirota equation and vortex filaments motion

被引：29

作者：

Demontis, F. ^{[1
]}

Ortenzi, G. ^{[2
,3
]}

van der Mee, C. ^{[1
]}

机构：

[1] Univ Cagliari, Dipartimento Matemat & Informat, I-09121 Cagliari, Italy

[2] Univ Bergamo, Dip Ingn Gest Informaz & Prod, I-24044 Dalmine, BG, Italy

[3] Univ Milano Bicocca, Dip Matemat Pura & Applicaz, I-20125 Milan, Italy

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2015年 / 313卷

关键词：

Soliton solutions; Vortex filaments; Inverse Scattering Transform; SOLITON; SYSTEMS;

D O I：

10.1016/j.physd.2015.09.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By using the Inverse Scattering Transform we construct an explicit soliton solution formula for the Hirota equation. The formula obtained allows one to get, as a particular case, the N-soliton solution, the breather solution and, most relevantly, a new class of solutions called multipole soliton solutions. We use these exact solutions to study the motion of a vortex filament in an incompressible Euler fluid with nonzero axial velocity. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：61 / 80

页数：20

共 48 条

[1]

Ablowitz M. J., 1981, Solitons and the Inverse Scattering Transform

[2]

Ablowitz M.J., 2004, Discrete and Continuous Nonlinear Schrodinger Systems, V302

[3] NONLINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS [J].