孤子耦合方程族的代数结构、自相溶源和守恒律（英文版）[AlgebraicStructures,self-consistentSourcesandConservationLaws:aCo
内容简介
The main contents of the book include the following： In chapter 2， we would liketo present a definition of the bi-integrable couplings of continuous and discrete solitonhierarchies， which contain two given integrable equations as their sub-systems. Thereare much richer mathematical structures behind bi-integrable couplings than scalarintegrable equations. And it is shown that such bi-integrable coupling system canpossess zero curvature representation and algebraic structure associated with semi-direct sums of Lie algebras. As application examples of the algebraic structure， thebi-integrable coupling system of the MKdV and generalized Toda lattice equationhierarchies are presented from this theory.
In chapter 3，it is shown that the Kronecker product of matrix Lie algebra canbe applied to construct a new integrable coupling system and Hamiltonian struc-tures of continuous and discrete soliton hierarchies. Furthermore， we construct theHamiltonian structure of integrable couplings of soliton hierarchy by using the Kro-necker product. The key steps aim at constructing a new Lax pairs by the Kroneckerproduct. As illustrate examples， direct application to the continuous and discretespectral problems lead to some novel soliton equation hierarchies of integrable cou-pling system. Then， we present the Hamiltonian structure of integrable couplings ofcontinuous and discrete hierarchies with the component-trace identity.