Multi-particle Dynamical Systems and Polynomials

被引：6

作者：

Demina, Maria V. ^{[1
]}

Kudryashov, Nikolai A. ^{[1
]}

机构：

[1] Natl Res Nucl Univ MEPhI, Kashirskoe Sh 31, Moscow 115409, Russia

来源：

REGULAR & CHAOTIC DYNAMICS | 2016年 / 21卷 / 03期

基金：

俄罗斯科学基金会;

关键词：

multi-particle dynamical systems; polynomial solutions of partial differential equations; orthogonal polynomials; PARTIAL-DIFFERENTIAL-EQUATIONS; POINT VORTICES; VORTEX SOURCES; EQUILIBRIA; ALGEBRA; MOTION;

D O I：

10.1134/S1560354716030072

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi-particle dynamical system by finding polynomial solutions of partial differential equations is introduced. The method enables one to integrate a wide class of polynomial multi-particle dynamical systems. The general solutions of certain dynamical systems related to linear second-order partial differential equations are found. As a by-product of our results, new families of orthogonal polynomials are derived.

引用

页码：351 / 366

页数：16

共 25 条

[1] CLASS OF POLYNOMIALS CONNECTED WITH KORTEWEG-DEVRIES EQUATION [J].

ADLER, M ;

MOSER, J .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1978, 61 (01) :1-30

[2] RATIONAL AND ELLIPTIC SOLUTIONS OF KORTEWEG DE-VRIES EQUATION AND A RELATED MANY-BODY PROBLEM [J].

AIRAULT, H ;

MCKEAN, HP ;

MOSER, J .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1977, 30 (01) :95-148

[3] Vortex crystals [J].

Aref, H ;

Newton, PK ;

Stremler, MA ;

Tokieda, T ;

Vainchtein, DL .

ADVANCES IN APPLIED MECHANICS, VOL 39, 2003, 39 :1-79

[4] Relative equilibria of point vortices and the fundamental theorem of algebra [J].

Aref, Hassan .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2011, 467 (2132) :2168-2184

[5]

Bartman A.B., 1984, NONLINEAR TURBULENT, V3, P1175

[6] The dynamics of three vortex sources [J].

Bizyaev, Ivan A. ;

Borisov, Alexey V. ;

Mamaev, Ivan S. .

REGULAR & CHAOTIC DYNAMICS, 2014, 19 (06) :694-701

[7] On the problem of motion of vortex sources on a plane [J].

Borisov, A. V. ;

Mamaev, I. S. .

REGULAR & CHAOTIC DYNAMICS, 2006, 11 (04) :455-466

[8] Multiparticle systems. The algebra of integrals and integrable cases [J].

Borisov, A. V. ;

Kilin, A. A. ;

Mamaev, I. S. .

REGULAR & CHAOTIC DYNAMICS, 2009, 14 (01) :18-41

[9] Dynamic interaction of point vortices and a two-dimensional cylinder [J].

Borisov, Alexey V. ;

Mamaev, Ivan S. ;

Ramodanov, Sergey M. .

JOURNAL OF MATHEMATICAL PHYSICS, 2007, 48 (06)

[10]

Borisov AV., 1998, REGUL CHAOTIC DYN, V3, P28, DOI 10.1070/rd1998v003n01ABEH000059

← 1 2 3 →