文章研究含变系数的广义浅水波(generalized shallow water wave)方程,该方程是对浅水波方程的一种推广,在物理学等领域具有更广泛的应用.首先使用WTC法检测该方程的Painlevé可积性,并利用Painlevé截断法构造自Bäcklund...文章研究含变系数的广义浅水波(generalized shallow water wave)方程,该方程是对浅水波方程的一种推广,在物理学等领域具有更广泛的应用.首先使用WTC法检测该方程的Painlevé可积性,并利用Painlevé截断法构造自Bäcklund变换,进而导出一系列新的解析解.同时使用李对称分析法求得无穷小生成子与李对称群,对该系统的相似约化方程、守恒律进行研究.展开更多
In this article,we study the meromorphic solutions of the following non-linear differential equation■where n and k are integers with n≥k≥3,P_(d)(z,f)is a differential polynomial in f of degree d≤n−1,p′js andα′j...In this article,we study the meromorphic solutions of the following non-linear differential equation■where n and k are integers with n≥k≥3,P_(d)(z,f)is a differential polynomial in f of degree d≤n−1,p′js andα′js are non-zero constants.We obtain the expressions of meromorphic solutions of the above equations under some restrictions onα′js.Some examples are given to illustrate the possibilities of our results.展开更多
文摘文章研究含变系数的广义浅水波(generalized shallow water wave)方程,该方程是对浅水波方程的一种推广,在物理学等领域具有更广泛的应用.首先使用WTC法检测该方程的Painlevé可积性,并利用Painlevé截断法构造自Bäcklund变换,进而导出一系列新的解析解.同时使用李对称分析法求得无穷小生成子与李对称群,对该系统的相似约化方程、守恒律进行研究.
基金supported by the National Natural Science Foundation of China(No.12001117)the Guangdong Basic and Applied Basic Research Foundation(No.2021A1515110654).
文摘In this article,we study the meromorphic solutions of the following non-linear differential equation■where n and k are integers with n≥k≥3,P_(d)(z,f)is a differential polynomial in f of degree d≤n−1,p′js andα′js are non-zero constants.We obtain the expressions of meromorphic solutions of the above equations under some restrictions onα′js.Some examples are given to illustrate the possibilities of our results.
