WKI族的高阶结构和二分量短脉冲方程
The higher grading structure of the WKI hierarchy and the two-component short pulse equation
摘要：
本文提出了可积族的一个高阶仿射代数构造，其中Wadati-Konno-Ichikawa（WKI）族是一个特例。我们表明，一个两个组件的推广的Sch\”afer-Wayne短脉冲方程产生很自然的第一个负流的WKI系列。还提出了一些新的可积非自治模型。守恒电荷，本地和非本地的，从Riccati形式的频谱问题。通过规范和倒易B”acklund变换，系统地构造了WKI族的环孤子解，建立了整个WKI族和AKNS族之间的精确联系.将短脉冲方程与sine-Gordon模型之间的联系推广到二分量短脉冲方程与Lund-Regge模型之间的对应。
英文摘要：
A higher grading affine algebraic construction of integrable hierarchies, containing the Wadati-Konno-Ichikawa (WKI) hierarchy as a particular case, is proposed. We show that a two-component generalization of the Sch\" afer-Wayne short pulse equation arises quite naturally from the first negative flow of the WKI hierarchy. Some novel integrable nonautonomous models are also proposed. The conserved charges, both local and nonlocal, are obtained from the Riccati form of the spectral problem. The loop-soliton solutions of the WKI hierarchy are systematically constructed through gauge followed by reciprocal B\" acklund transformation, establishing the precise connection between the whole WKI and AKNS hierarchies. The connection between the short pulse equation with the sine-Gordon model is extended to a correspondence between the two-component short pulse equation and the Lund-Regge model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
