规范变换与有限维可积系统间的变换

本文表明，利用两个特征值问题的规范变换，不仅可以建立和它们相联系的势的约束之间以及相应的有限维Ｈａｍｉｌｔｏｎ系统间的变换关系式，而且可以由一个可积系统的对合守恒积分导出另一个系统的守恒积分     

ON COMPLETE INTEGRABILITY OF A HIERARCHY OF FINITE-DIMENSIONAL HAMILTONIAN SYSTEMS

A hierarchy of Hamiltonian systems obtained from the Lax pair of KdV hierarchy under theconstraint condition on potential u = (q, q) is. presented. The independent integrals for theseHamiltonian systems are constructed by using recursion operator and shown to be in involution.Thus this hierarchy of Hamiltonian systems is completely integrable in the sense of Liouville. andthey commute with each other.     

带附加项的AKNS方程族的Darboux变换

本文了带附加项的ＡＫＮＳ方程族，给出了其Ｌａｘ表示，守恒律和Ｄａｒｂｏｕｘ变换。     

RESTRICTED FLOWS OF A HIERARCHYOF INTEGRABLE DISCRETE SYSTEMS

1.IntroductionTherestrictedflowsofsolitonhierarchyhavebeenextensivelystudied(see,forexample,[1--7]).Theapproachforconstructingrestrictedflowsofsolitonhierarchycanalsobeappliedtoobtainrestrictedflows(discretemaps)ofahierarchyofdiscreteintegrablesystems(nonlineardifferential-differenceequations)IS,9].TheserestrictedflowshavetheformofLagrangeequationsandthereforecanmodelphysicallyinterestingprocesses.Wesupposethatthehierarchyofdiscreteintegrablesystems(DIS)isassociatedwithadiscreteisospectralp…     

Zakharov-Shabat 特征值问题及 AKNS 型发展方程的非线性迭加公式

在非线性发展方程中，为了由方程的已知解求出它的另一些解，给出这些方程的Bcklund变换以及由此而导出的非线性迭加公式是一个十分重要的方法。目前已有不     

A Simple Method for Generating Discrete Multi-Component Integrable Hierarchy

For M×N spectral matrix, a kind of operation ？ which satisfies combination law （a？b）？c=a？（b？c） is introduced. The discrete multi？component zero-curvature equation is deduced by using the new operation ？, and a simple method for constructing discrete multi-component integrable hierarchy is proposed. As its application, the multi-component Toda hierarchy and its two kinds of integrable couplings are worked out.     

Solving AKNS equations via Jacobi inversion problem

1.IntroductionRecelltlymuchworkhasbeencarriedoutinthestudyoftheseparationofvariablesofacompletelyintegrableHalniltoniansystemll--6].Forclassicalilltegrablesystemssubjecttoinversescatteringtransformationthestandardconstructionoftheaction-anglevariablesusingthepolesoftheBaker-Anheizerfullctionisequivalenttotheseparationofvariablesl31.Theabategapsolutionsofthesolitonequationsareconstructedduetotheseparationofvariablesofthestationarysolitonequationsll].Forsomekindoffinite-dimensionalintegrableHt…     

非线性发展方程的转换算子Ⅲ

<正> 这篇文章是非线性发展方程的转换算子Ⅰ和Ⅱ的继续.在文献[3]中,Захаров等利用了一个不含参数ξ的规范变换(但未求出这种变换的具体形式)和在变换下散射量的一些性质建立了非线性 Schr(?)dinger 方程     

Bäcklund变换的递推算子之间的转换算子I

本文首先通过引入递推算子之间的转换算子,证明了两类Bäcklund交换是等价变换及相应的两类发展方程是等价方程;其次利用特征值问题存在的规范变换,得到了这些方程的无穷守恒律的密度和流的关系;最后借助一个新的泛函求导公式,从一类发展方程的Hamilton形式导出另一类发展方程的Hamilton形式。     

A HIERARCHY OF INTEGRABLE HAMILTONIAN SYSTEMS WITH NEUMANN TYPE CONSTRAINT

A hierarchy of integrable Hamiltonian systems with Neumann type constraint isobtained by restricting a hierarchy of evolution equations associated with λφ_(xx)+u_iλ~iφ=λ~mφ to aninvariant subspace of their recursion operator.The independentintegrals of motion and Hamiltonian functions for these Hamiltonian systems areconstructed by using relevant reeursion formula and are shown to be in involution.Thusthese Hamiltonian systems are completely integrable and commute with each other.