一类孤子族的Lax表示

The Lax Representation of a Hierarchy of Soliton Equations

对一类特征值问题定义映射σ给出一个Ｌａｘ对Ｕ，Ｖｍ，其相应的Ｌｅｎａｒｄ序列Ｋξｊ－１＝Ｊξｊ不含逆微分算子－１，可显式求出线性表示的通解ξｍ＝Σｃｓｇｍ－ｓ，从而得到了一类显式表示的孤子族αｔｍ＝Ｘｍ．

For some eigenvalue problem, a map is defined to give the Lax pairs for a hierarchy of soliton equations. The inverse differential operator  -1 is not contained in the corresponding Lenard's equations Kξ j-1 =Jξ j. The explicit general solutions of the Lenard's equations are linearly represented, by which the hierarchy of soliton equations is derived in explicit form.