Generations of Integrable Hierarchies and Exact Solutions of Related Evolution Equations with Variable Coefficients

We first propose a way for generating Lie algebras from which we get a few kinds of reduced 6 6 Lie algebras, denoted by R6, R8 and R1,R6/2, respectively. As for applications of some of them, a Lax pair is introduced by using the Lie algebra R6 whose compatibility gives rise to an integrable hierarc...

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Bibliographic Details
Published in:Acta Mathematicae Applicatae Sinica 2014-10, Vol.30 (4), p.1085-1106
Main Authors: Zhang, Yu-feng, Wang, Yan, Feng, Bin-lu, Mei, Jian-qin
Format: Article
Language:English
Subjects:
Applications of Mathematics
Hamilton结构
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
mKdV方程
Theoretical
世代
变系数
演化方程
积层
精确解
非线性方程
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Summary:We first propose a way for generating Lie algebras from which we get a few kinds of reduced 6 6 Lie algebras, denoted by R6, R8 and R1,R6/2, respectively. As for applications of some of them, a Lax pair is introduced by using the Lie algebra R6 whose compatibility gives rise to an integrable hierarchy with 4- potential functions and two arbitrary parameters whose corresponding Hamiltonian structure is obtained by the variational identity. Then we make use of the Lie algebra R6 to deduce a nonlinear integrable coupling hierarchy of the mKdV equation whose Hamiltonian structure is also obtained. Again,via using the Lie algebra R62, we introduce a Lax pair and work out a linear integrable coupling hierarchy of the mKdV equation whose Hamiltonian structure is obtained. Finally, we get some reduced linear and nonlinear equations with variable coefficients and work out the elliptic coordinate solutions, exact traveling wave solutions, respectively.
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-014-0445-1