无色散BKP方程族可积耦合推广及其求解  

On the Ingegrable Coupled Generalization of Dispersionless BKP Hierarchy and Its Solutions

作　　者：刘晶鑫[1] 吴红霞[1] 曾云波[2] Liu Jingxin Wu Hongxia Zeng Yunbo(Department of Mathematics, Jimei University, Fujian Xiamen 361021 Department of Mathematical, Tsinghua University, Beijing 100084)

机构地区：[1]集美大学理学院数学系,福建厦门361021 [2]清华大学数学科学系,北京100084

出　　处：《数学物理学报（A辑）》2017年第2期313-325,共13页Acta Mathematica Scientia

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~~

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.The symmetry constraint for dispersionless BKP （dBKP） hierarchy is firstly de- rived 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.

关 键 词：无色散BKP方程族 推广 对称约束 带自相容源的无色散BKP方程族 速端解. 

分 类 号：O29[理学—应用数学]