We firstly propose two kinds of new multi-component BKP （mcBKP） hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with ...We firstly propose two kinds of new multi-component BKP （mcBKP） hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with self-consistent sources whose Lax representations are presented. The two mcBKP hierarchies both admit reductions to the k-constrained BKP hierarchy and to integrable （1＋1）-dimensional hierarchy with self-consistent sources, which include two types of SK equation with self-consistent sources and of hi-directional SK equations with self-consistent展开更多
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...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.展开更多
基金supported by National Basic Research Program of China (973 Program) under Grant No.2007CB814800National Natural Science Foundation of China under Grant No.10601028the Natural Science Foundation of Fujian Province under Grant No.2008J0199
文摘We firstly propose two kinds of new multi-component BKP （mcBKP） hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with self-consistent sources whose Lax representations are presented. The two mcBKP hierarchies both admit reductions to the k-constrained BKP hierarchy and to integrable （1＋1）-dimensional hierarchy with self-consistent sources, which include two types of SK equation with self-consistent sources and of hi-directional SK equations with self-consistent
文摘该文通过对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.
