A Generalized Dressing Approach for Solving the Extended KP and the Extended mKP Hierarchy
A Generalized Dressing Approach for Solving the Extended KP and the Extended mKP Hierarchy
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DOI：
10.1063/1.3126494
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发表时间：
2009-05
影响因子：
1.3
通讯作者：
Xiaojun Liu;Runliang Lin;Bo Jin;Yunbo Zeng
中科院分区：
文献类型：
--
作者：
Xiaojun Liu;Runliang Lin;Bo Jin;Yunbo Zeng
利用修饰法和常数变换法相结合的方法以及构造特征函数的公式来求解扩展的KP族，它是基于KP族的对称性约束的一个多序列时间流的族。类似地，建立了扩展的MKP族，给出了它的零曲率形式、Lax表示和约化。通过规范变换，可以很容易地将扩展的KP族的修饰解转化为扩展的MKP族的解。显式构造了扩展KP族和扩展MKP族的Wronskian解。
A combination of dressing method and variation of constants as well as a formula for constructing the eigenfunction is used to solve the extended KP hierarchy, which is a hierarchy with one more series of time flow and based on the symmetry constraint of KP hierarchy. Similarly, extended mKP hierarchy is formulated and its zero-curvature form, Lax representation, and reductions are presented. Via gauge transformation, it is easy to transform dressing solutions of extended KP hierarchy to the solutions of extended mKP hierarchy. Wronskian solutions of extended KP and extended mKP hierarchies are constructed explicitly.