Generations of integrable hierarchies and exact solutions of related evolution equations with variable coefficients

Autor:	Yufeng Zhang, Yan Wang, Jian-qin Mei, Bin-lu Feng
Rok vydání:	2014
Předmět:	Pure mathematics Adjoint representation of a Lie algebra Nonlinear Sciences::Exactly Solvable and Integrable Systems Applied Mathematics Lax pair Mathematical analysis Lie algebra Adjoint representation Current algebra Weight Affine Lie algebra Mathematics Lie conformal algebra
Zdroj:	Acta Mathematicae Applicatae Sinica, English Series. 30:1085-1106
ISSN:	1618-3932 0168-9673
Popis:	We first propose a way for generating Lie algebras from which we get a few kinds of reduced Lie algebras, denoted by R6, R8 and R16,R26, 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 R16 to deduce a nonlinear integrable coupling hierarchy of the mKdV equation whose Hamiltonian structure is also obtained. Again,via using the Lie algebra R26, 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::9893c8d67e8deceb9a32a3fcc488970c https://doi.org/10.1007/s10255-014-0445-1 Zobrazit plný text záznamu Full text from SpringerLink