Special transformation properties for certain equations with applications in Plasma Physics

被引：3

作者：

Charalambous, Kyriacos ^{[1
,2
]}

Sophocleous, Christodoulos ^{[2
]}

机构：

[1] Univ Nicosia, Dept Math, Nicosia, Cyprus

[2] Univ Cyprus, Dept Math & Stat, CY-1678 Nicosia, Cyprus

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2021年 / 44卷 / 18期

关键词：

equivalence transformations; linearization; potential symmetries; system of diffusion equations; REACTION-DIFFUSION EQUATIONS; MASS-TRANSFER EQUATIONS; GROUP CLASSIFICATION; LIE SYMMETRIES; EQUIVALENCE TRANSFORMATIONS; POTENTIAL SYMMETRIES; SYSTEMS; LINEARIZATION; MATRIX;

D O I：

10.1002/mma.7742

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Nonlocal transformation properties are derived for a nonlinear system which appears in certain problems in Plasma Physics. Such properties exist since the system admits conservation laws. These conservation laws lead to auxiliary systems which are studied in the point of view of equivalence transformations and Lie point symmetry analysis. The existence of infinite dimensional symmetries, in some cases, leads to the construction of linearizing mappings.

引用

页码：14776 / 14790

页数：15

共 35 条

[1] A system of degenerate parabolic equations from plasma physics: The large time behavior [J].

Bertsch, M ;

Kamin, S .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2000, 31 (04) :776-790

[2] ON THE REMARKABLE NON-LINEAR DIFFUSION EQUATION (DELTA-DELTA-X)(A(U+B)-2(DELTA-U-DELTA-X))-(DELTA-U-DELTA-T) = 0 [J].

BLUMAN, G ;

KUMEI, S .

JOURNAL OF MATHEMATICAL PHYSICS, 1980, 21 (05) :1019-1023

[3] USE AND CONSTRUCTION OF POTENTIAL SYMMETRIES [J].

BLUMAN, G .

MATHEMATICAL AND COMPUTER MODELLING, 1993, 18 (10) :1-14

[4]

Bluman G. W., 2013, Symmetries and Differential Equations, V81

[5] NEW CLASSES OF SYMMETRIES FOR PARTIAL-DIFFERENTIAL EQUATIONS [J].

BLUMAN, GW ;

REID, GJ ;

KUMEI, S .

JOURNAL OF MATHEMATICAL PHYSICS, 1988, 29 (04) :806-811

[6] Group analysis of the generalized Burnett equations [J].

Bobylev, Alexander V. ;

Meleshko, Sergey V. .

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2020, 27 (03) :494-508

[7] Lie symmetries of a system arising in plasma physics [J].

Charalambous, K. ;

Sophocleous, C. .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (04) :1331-1343

[8] Non-linear reaction-diffusion systems with variable diffusivities: Lie symmetries, ansatze and exact solutions [J].

Cherniha, R ;

King, JR .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 308 (01) :11-35

[9] Lie symmetries of nonlinear multidimensional reaction-diffusion systems: II [J].

Cherniha, R ;

King, JR .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (02) :405-425

[10] Lie symmetries of nonlinear multidimensional reaction-diffusion systems: I [J].

Cherniha, R ;

King, JR .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2000, 33 (02) :267-282

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