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Conditional Lie‐Bäcklund Symmetry of Evolution System and Application for Reaction‐Diffusion System
Author(s) -
Ji Lina,
Qu Changzheng,
Shen Shoufeng
Publication year - 2014
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12042
Subject(s) - mathematics , nonlinear system , invariant (physics) , symmetry (geometry) , ordinary differential equation , reaction–diffusion system , lie group , exponential function , polynomial , mathematical analysis , partial differential equation , differential equation , mathematical physics , pure mathematics , physics , quantum mechanics , geometry
Conditional Lie‐Bäcklund symmetry (CLBS) method is developed to study system of evolution equations. It is shown that reducibility of a system of evolution equations to a system of ordinary differential equations can be fully characterized by the CLBS of the considered system. As an application of the approach, a class of two‐component nonlinear diffusion equations is studied. The governing system and the admitted CLBS can be identified. As a consequence, exact solutions defined on the polynomial, exponential, trigonometric, and mixed invariant subspaces are constructed due to the corresponding symmetry reductions.
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