A new Lie algebra G of the Lie algebra sl(2) is constructed with complex entries whose structure constantsare real and imaginary numbers.A loop algebra G corresponding to the Lie algebra G is constructed,for which iti...A new Lie algebra G of the Lie algebra sl(2) is constructed with complex entries whose structure constantsare real and imaginary numbers.A loop algebra G corresponding to the Lie algebra G is constructed,for which itis devoted to generating a soliton hierarchy of evolution equations under the framework of generalized zero curvatureequation which is derived from the compatibility of the isospectral problems expressed by Hirota operators.Finally,wedecompose the Lie algebra G to obtain the subalgebras G_1 and G_2.Using the G_2 and its one type of loop algebra (?)_2,aLiouville integrable soliton hierarchy is obtained,furthermore,we obtain its bi-Hamiltonian structure by employing thequadratic-form identity.展开更多
基金The National Natural Science Foundation of China(1127100861072147+1 种基金11071159)the Shanghai University Leading Academic Discipline Project(A13-0101-12-004)
基金Supported in part by the National Natural Science Foundation of China(11401424)the Natural Science Foundation of Shanxi province(201901D211423)+1 种基金the Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi(2019L0783)the Teaching Reform project of Taiyuan Normal University(JGLX2128)。
基金supported by the National Natural Science Foundation of China under Grant No.10471139
文摘A new Lie algebra G of the Lie algebra sl(2) is constructed with complex entries whose structure constantsare real and imaginary numbers.A loop algebra G corresponding to the Lie algebra G is constructed,for which itis devoted to generating a soliton hierarchy of evolution equations under the framework of generalized zero curvatureequation which is derived from the compatibility of the isospectral problems expressed by Hirota operators.Finally,wedecompose the Lie algebra G to obtain the subalgebras G_1 and G_2.Using the G_2 and its one type of loop algebra (?)_2,aLiouville integrable soliton hierarchy is obtained,furthermore,we obtain its bi-Hamiltonian structure by employing thequadratic-form identity.
