A new simple loop algebra GM is constructed, which is devoted to establishing an isospectral problem.By making use of generalized Tu scheme, the multi-component SC hierarchy is obtained. Furthermore, an expanding loop...A new simple loop algebra GM is constructed, which is devoted to establishing an isospectral problem.By making use of generalized Tu scheme, the multi-component SC hierarchy is obtained. Furthermore, an expanding loop algebra FM of the loop algebra GM is presented. Based on FM, the multi-component integrable coupling system of the multi-component SC hierarchy of soliton equations is worked out. How to design isospectral problem of mulitcomponent hierarchy of soliton equations is a technique and interesting topic. The method can be applied to other nonlinear evolution equations hierarchy.展开更多
<正> A new loop algebra containing four arbitrary constants is presented,whose commutation operation isconcise,and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in...<正> A new loop algebra containing four arbitrary constants is presented,whose commutation operation isconcise,and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this paper,which can be reduced to computing formula of constant γ in the trace identity.As application,a new Liouville integrablehierarchy,which can be reduced to AKNS hierarchy is derived.展开更多
Under the frame of the (2+1)-dimensional zero curvature equation and Tu model, the (2+1)-dimensional dispersive long wave hierarchy is obtained. Furthermore, the loop algebra is expanded into a larger one. Moreover, a...Under the frame of the (2+1)-dimensional zero curvature equation and Tu model, the (2+1)-dimensional dispersive long wave hierarchy is obtained. Furthermore, the loop algebra is expanded into a larger one. Moreover, a class of integrable coupling system for dispersive long wave hierarchy and (2+1)-dimensional multi-component integrable system will be investigated.展开更多
文摘A new simple loop algebra GM is constructed, which is devoted to establishing an isospectral problem.By making use of generalized Tu scheme, the multi-component SC hierarchy is obtained. Furthermore, an expanding loop algebra FM of the loop algebra GM is presented. Based on FM, the multi-component integrable coupling system of the multi-component SC hierarchy of soliton equations is worked out. How to design isospectral problem of mulitcomponent hierarchy of soliton equations is a technique and interesting topic. The method can be applied to other nonlinear evolution equations hierarchy.
文摘<正> A new loop algebra containing four arbitrary constants is presented,whose commutation operation isconcise,and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this paper,which can be reduced to computing formula of constant γ in the trace identity.As application,a new Liouville integrablehierarchy,which can be reduced to AKNS hierarchy is derived.
文摘Under the frame of the (2+1)-dimensional zero curvature equation and Tu model, the (2+1)-dimensional dispersive long wave hierarchy is obtained. Furthermore, the loop algebra is expanded into a larger one. Moreover, a class of integrable coupling system for dispersive long wave hierarchy and (2+1)-dimensional multi-component integrable system will be investigated.
