Ermakov-Painleve II Reduction in Cold Plasma Physics. Application of a Backlund Transformation

被引：13

作者：

Rogers, Colin ^{[1
]}

Clarkson, Peter A. ^{[2
]}

机构：

[1] Univ New South Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

[2] Univ Kent, Sch Math Stat & Actuarial Sci, Canterbury CT2 7FS, Kent, England

来源：

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS | 2018年 / 25卷 / 02期

关键词：

NONLINEAR SCHRODINGER-EQUATION; MOVING BOUNDARY-PROBLEMS; SOLUTION HIERARCHIES; HYDROMAGNETIC-WAVES; 2ND; PROPAGATION; SYSTEMS; EVOLUTION; GEOMETRY; NLS;

D O I：

10.1080/14029251.2018.1452672

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A class of symmetry transformations of a type originally introduced in a nonlinear optics context is used here to isolate an integrable Ermakov-Painleve II reduction of a resonant NLS equation which encapsulates a nonlinear system in cold plasma physics descriptive of the uni-axial propagation of magneto-acoustic waves. A Backlund transformation is employed in the iterative generation of novel classes of solutions to the cold plasma system which involve either Yablonski-Vorob'ev polynomials or classical Airy functions.

引用

页码：247 / 261

页数：15

共 25 条

[1] Ermakov-Painlevé II Reduction in Cold Plasma Physics. Application of a Bäcklund Transformation
Colin Rogers
Peter A. Clarkson
[J]. Journal of Nonlinear Mathematical Physics, 2018, 25 : 247 - 261
[2] On Ermakov-Painleve II systems. Integrable reduction
Rogers, Colin
Schief, Wolfgang K.
[J]. MECCANICA, 2016, 51 (12) : 2967 - 2974
[3] Ermakov-Painleve II Symmetry Reduction of a Korteweg Capillarity System
Rogers, Colin
Clarkson, Peter A.
[J]. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2017, 13
[4] On Hybrid Ermakov-Painleve Systems. Integrable Reduction
Rogers, Colin
[J]. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2017, 24 (02) : 239 - 249
[5] ON A ERMAKOV-PAINLEVE II REDUCTION IN THREE-ION ELECTRODIFFUSION. A DIRICHLET BOUNDARY VALUE PROBLEM
Amster, Pablo
Rogers, Colin
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2015, 35 (08) : 3277 - 3292
[6] On a Painleve II model in steady electrolysis: Application of a backlund transformation
Rogers, C
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[7] The resonant nonlinear Schrodinger equation in cold plasma physics. Application of Backlund-Darboux transformations and superposition principles
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Rogers, C.
Schief, W. K.
[J]. JOURNAL OF PLASMA PHYSICS, 2007, 73 (02) : 257 - 272
[8] ANovel Ermakov-Painleve II System: N+1-Dimensional Coupled NLS and Elastodynamic Reductions
Rogers, Colin
[J]. STUDIES IN APPLIED MATHEMATICS, 2014, 133 (02) : 214 - 231
[9] Backlund transformations and Painleve analysis: Exact soliton solutions for strongly rarefied relativistic cold plasma
Khater, AH
Callebaut, DK
Shamardan, AB
Ibrahim, RS
[J]. PHYSICS OF PLASMAS, 1997, 4 (11) : 3910 - 3922
[10] Backlund transformation of partial differential equations from the Painleve-Gambier classification. II. Tzitzeica equation
Conte, R
Musette, M
Grundland, AM
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 1999, 40 (04) : 2092 - 2106

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