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On a new generalization of dispersionless Kadomtsev–Petviashvili hierarchy and its reductions
Author(s) -
Wu Hongxia,
Zeng Yunbo
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2878
Subject(s) - kadomtsev–petviashvili equation , mathematics , type (biology) , hierarchy , generalization , dispersionless equation , mathematical physics , pure mathematics , mathematical analysis , partial differential equation , burgers' equation , ecology , economics , market economy , biology
The dispersionless Kadomtsev–Petviashvili hierarchy is generalized by introducing two new time series γ n and σ k with two parameters η n and λ k . By this hierarchy, we obtain the first type, the second type as well as mixed type of dispersionless Kadomtsev–Petviashvili equation with self‐consistent sources and their related conservation equations. In addition, the reduction and constrained flow of this new hierarchy are studied. The first type, the second type and the mixed type of dispersionless Korteweg–de Vries equation with self‐consistent sources and of dispersionless Boussinesq equation with self‐consistent sources are obtained. Copyright © 2013 John Wiley & Sons, Ltd.