A new method is presented to generate finite dimensional integrable systems.Our starting point is a generalized Lax matrix instead of usual Lax pair.Then a unisonant r-matrix structure and a set of generalized Hamilto...A new method is presented to generate finite dimensional integrable systems.Our starting point is a generalized Lax matrix instead of usual Lax pair.Then a unisonant r-matrix structure and a set of generalized Hamiltonian functions are constructed.It can be clearly seen that various constrained integrable Hows by nonlinearization method,such as the c-AKNS,c-MKdV,c~Toda,etc.,are derived from the reduction of this structure.Furthermore,some new integrable Hows are produced.展开更多
基金Supported by the Alexander von Humbold t Foundation,Germanythe Chinese National Basic Reseach Projec t“Nonlinear Science”,Special Grant of Excellent Ph.D.Thesis and Doctoral Programme Foundation of the Institution of High Education of China,the Science&Technology Foundation(Youth Talent Foundation)and the Science Research Foundation of Education Committee of Liaoning Province of ChinaThe author would like to express his sincere thanks to Professor Strampp Walter for his warm invitation and hospitality.
文摘A new method is presented to generate finite dimensional integrable systems.Our starting point is a generalized Lax matrix instead of usual Lax pair.Then a unisonant r-matrix structure and a set of generalized Hamiltonian functions are constructed.It can be clearly seen that various constrained integrable Hows by nonlinearization method,such as the c-AKNS,c-MKdV,c~Toda,etc.,are derived from the reduction of this structure.Furthermore,some new integrable Hows are produced.
