An explicit N-flod Darboux transformation for evolution equations determined by general 2×2 AKNS system is constructed.By using the Darboux transformation,the solutions of the evolution equations are reduced to s...An explicit N-flod Darboux transformation for evolution equations determined by general 2×2 AKNS system is constructed.By using the Darboux transformation,the solutions of the evolution equations are reduced to solving a linear algebraic system,from which a unified and explicit formulation of 2N-soliton solutions for the evolution equation are given.Furthermore,a reduction, technique for MKdV equation is presented.and an N-fold Darboux transformation of MKdV hierarchy is constructed through the reduction technique.A Maple package which can entirely automatically output the exact N-soliton solutions of the MKdV equation is developed.展开更多
文摘An explicit N-flod Darboux transformation for evolution equations determined by general 2×2 AKNS system is constructed.By using the Darboux transformation,the solutions of the evolution equations are reduced to solving a linear algebraic system,from which a unified and explicit formulation of 2N-soliton solutions for the evolution equation are given.Furthermore,a reduction, technique for MKdV equation is presented.and an N-fold Darboux transformation of MKdV hierarchy is constructed through the reduction technique.A Maple package which can entirely automatically output the exact N-soliton solutions of the MKdV equation is developed.
