无色散BKP方程族可积耦合推广及其求解

发布时间：2018-06-03 07:39

  本文选题：无色散BKP方程族 + 推广　； 参考：《数学物理学报》2017年02期

【摘要】：该文通过对B类Kadomtsev-Petviashvili(B type of Kadomtsev-Petviashvili,简称为BKP)方程族基于特征函数及共轭特征函数表示的对称约束取无色散极限,得到无色散BKP(dispersionless BKP,简称为dBKP)方程族的对称约束;其次,基于dBKP方程族的对称约束,考察了dBKP方程族的推广问题.通过计算推广的dBKP方程族的零曲率方程,该文导出了第一、二类型的带自相容源的dBKP方程(dispersionless BKP equation with selfconsistent sources,简称为dBKPESCS)及其相应的守恒方程.最后,利用速端变换及约化的方法求解了第一型dBKPESCS.
[Abstract]:In this paper, the symmetric constraints of class B Kadomtsev-Petviashvili(B type of Kadomtsev-Petviashvili equations based on eigenfunction and conjugate eigenfunction are obtained, and the symmetric constraints of the class B Kadomtsev-Petviashvili(B type of Kadomtsev-Petviashvili equations are obtained. Based on the symmetric constraints of the dBKP equation family, the extension of the dBKP equation family is investigated. By calculating the zero curvature equations of the generalized dBKP equation family, the first and second types of dBKP equation with self-compatible source are derived in this paper. The BKP equation with selfconsistent sources, is called dBKPESCS for short) and its corresponding conservation equations are derived. Finally, the first type dBKPESCSs are solved by the method of fast end transformation and reduction.
【作者单位】： 集美大学理学院数学系;清华大学数学科学系;
【基金】：国家自然科学基金(11201178) 福建省出国留学奖学金和集美大学科研启动基金~~
【分类号】：O175.29
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本文编号：1972011