LINEARIZABILITY AND NONLOCAL SUPERPOSITION FOR NONLINEAR TRANSPORT EQUATION WITH MEMORY

被引：2
作者：
Rzeszut, W. [1 ]
Tertyshnyk, O. [2 ]
Tychynin, V. [2 ]
Vladimirov, V. [3 ]
机构：
[1] Jagiellonian Univ, Fac Math & Comp Sci, PL-30348 Krakow, Poland
[2] Prydniprovska State Acad Civil Engn & Architectur, UA-49005 Dnepropetrovsk, Ukraine
[3] AGH Univ Sci & Technol, Fac Appl Math, PL-30059 Krakow, Poland
来源：
REPORTS ON MATHEMATICAL PHYSICS | 2013年 / 72卷 / 02期
关键词：
nonlinear transport equation; effects of memory; potential symmetry; nonlocal linearization; exact solutions; nonlinear superposition principle; GENERATION; SYMMETRIES;
D O I：
10.1016/S0034-4877(14)60016-1
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Potential symmetry of a class of nonlinear transport equations taking into account the effects of memory is studied. For a specific transport coefficient the symmetry is shown to be infinite. This fact is used for constructing nonlocal transformation linearizing the transport equation. New formulae of nonlocal nonlinear superposition and generation of solutions are proposed. Additional Lie symmetries of the corresponding linear equations are used to construct nonlocal symmetries of the source equation. The formulae derived are used for the construction of exact solutions.
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收藏
页码：235 / 252
页数：18
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