【摘要】 本文研究Jaulent-Miodek族的对易表示,在无反射位势的特征函数表示:即 q=-〈ψ₂,ψ₂〉,r=（Aψ₂,ψ2）; （q,r）^T≡f（ψ）,ψ≡（ψ₁,ψ₂）^T所诱导的约束条件下,Jaulent-Miodek族的Lax对的空间部分被非线性化为一个完全可积系统(R^2N,dψ₁∧dψ₂,H=（?）₀),其中（?）₀=i〈Aψ₁,ψ₂〉+1/2〈ψ₁,ψ₂〉〈Aψ₂,ψ₂〉.时间部分的非线性化导出它的N-对合系{（?）_m},相容方程组（（?）₀）,（（?）_m）的对合解被f映为第m个Jaulent-Miodek方程的解。更多还原

【Abstract】 In this paper, the commutative representation of the Jaulent-Miodek Hierarchy is discussed. Under the constrained condition induced by the eigenfunction expression of the reflectionless potentialthe spatial part of the Lax pair of the Jaulent-Miodek equation is nonlinearized to be a comletely in-tegrable systemwhile the nonlinearization of the time part leads to its N-involutive system {Fm} . The involutive solution of the compatible system (F0). (Fm) is mapped by / into the solution of the m -th Jaulent-Miodek equation.更多还原