An integrable （2＋1）-dimensional coupled mKdV equation is decomposed into two （1 ＋1）-dimensional soliton systems, which is produced from the compatible condition of three spectral problems. With the help of decom...An integrable （2＋1）-dimensional coupled mKdV equation is decomposed into two （1 ＋1）-dimensional soliton systems, which is produced from the compatible condition of three spectral problems. With the help of decomposition and the Darboux transformation of two （1＋1）-dimensional soliton systems, some interesting explicit solutions of these soliton equations are obtained.展开更多
Two kinds of higher-dimensional Lie algebras and their loop algebras are introduced, for which a few expanding integrable models including the coupling integrable couplings of the Broer-Kaup （BK） hierarchy and the d...Two kinds of higher-dimensional Lie algebras and their loop algebras are introduced, for which a few expanding integrable models including the coupling integrable couplings of the Broer-Kaup （BK） hierarchy and the dispersive long wave （DLW） hierarchy as well as the TB hierarchy are obtained. From the reductions of the coupling integrable couplings, the corresponding coupled integrable couplings of the BK equation, the DLW equation, and the TB equation are obtained, respectively. Especiaily, the coupling integrable coupling of the TB equation reduces to a few integrable couplings of the well-known mKdV equation. The Hamiltonian structures of the coupling integrable couplings of the three kinds of soliton hierarchies are worked out, respectively, by employing the variationai identity. Finally, we decompose the BK hierarchy of evolution equations into x-constrained flows and tn-eonstrained flows whose adjoint representations and the Lax pairs are given.展开更多
In this paper, we study a coupled modified Volterra lattice equation which is an integrable semidiscrete version of the coupled KdV and the coupled mKdV equation. By using the Darboux transformation, we obtain its new...In this paper, we study a coupled modified Volterra lattice equation which is an integrable semidiscrete version of the coupled KdV and the coupled mKdV equation. By using the Darboux transformation, we obtain its new explicit solutions including multi-soliton and multi-positon. Furthermore, an integrable discretization of the coupled modified Volterra lattice equation is constructed.展开更多
基金Project Supported by the Natural Science Foundation of China(11261037)the High Education Science Research Program of China(211034)the High Education Science Research Program of Inner Mongolia Autonomous Region,China(NJ10045)
基金the Special Funds for Major State Basic Research Project of China under No.G2000077301
文摘An integrable （2＋1）-dimensional coupled mKdV equation is decomposed into two （1 ＋1）-dimensional soliton systems, which is produced from the compatible condition of three spectral problems. With the help of decomposition and the Darboux transformation of two （1＋1）-dimensional soliton systems, some interesting explicit solutions of these soliton equations are obtained.
基金Supported by the National Science Foundation of China under Grant No.10971031the Natural Science Foundation of Shandong Province under Grant No.ZR2009AL021
文摘Two kinds of higher-dimensional Lie algebras and their loop algebras are introduced, for which a few expanding integrable models including the coupling integrable couplings of the Broer-Kaup （BK） hierarchy and the dispersive long wave （DLW） hierarchy as well as the TB hierarchy are obtained. From the reductions of the coupling integrable couplings, the corresponding coupled integrable couplings of the BK equation, the DLW equation, and the TB equation are obtained, respectively. Especiaily, the coupling integrable coupling of the TB equation reduces to a few integrable couplings of the well-known mKdV equation. The Hamiltonian structures of the coupling integrable couplings of the three kinds of soliton hierarchies are worked out, respectively, by employing the variationai identity. Finally, we decompose the BK hierarchy of evolution equations into x-constrained flows and tn-eonstrained flows whose adjoint representations and the Lax pairs are given.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10971136also in part by the Ministry of Education and Innovation of Spain under Contract MTM2009-12670ZHQ is supported by Shanghai 085 Project
文摘In this paper, we study a coupled modified Volterra lattice equation which is an integrable semidiscrete version of the coupled KdV and the coupled mKdV equation. By using the Darboux transformation, we obtain its new explicit solutions including multi-soliton and multi-positon. Furthermore, an integrable discretization of the coupled modified Volterra lattice equation is constructed.
