无色散BKP方程族可积耦合推广及其求解

摘要

The symmetry constraint for dispersionless BKP (dBKP) hierarchy is firstly derived by taking dispersionless limit of that for BKP hierarchy.Then,based on the symmetry constraint for dBKP hierarchy,a new extended dBKP hierarchy is constructed.In addition,the integrability of this new extended dBKP hierarchy is proved by presenting its zero-curvature equation and the related conservation equation.From its zero-curvature equation,two types of dBKP equations with self-consistent sources (dBKPESCS) together with their associated conservation equations are obtained.Hodograph solutions for the first type of dBKPESCS are finally obtained.%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 self-consistent 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.