Painleve analysis and exact solutions of the BoussinesqBurgers equation 

Author  LiJinWei 
Tutor  ZhangJinShun 
School  Huaqiao University 
Course  Basic mathematics 
Keywords  BoussinesqBurgers equation Painleve test resonances Darboux Backlund transformation Schwarzian derivative equation 
CLC  O175.29 
Type  Master's thesis 
Year  2009 
Downloads  44 
Quotes  0 
Painleve analysis is a useful method in soliton theory. It can be used to prove integrability and find solutions of nonlinear partial differential equations.In this thesis, the (1+1) and (2+1) dimensional BoussinesqBurgers equations(BB equation) are studied by means of the Painleve analysis. Some DarbouxBacklund transformations are obtained. The main results are arranged as following.(1). Painleve test is used to study the (1+1) dimensional BB equationFour branches are obtained from the Painleve analylsis. The branches are studied one by one. Their Painleve propertys are proved and DarbouxBacklund transformations are obtained. Through DarbouxBacklund transformations, some properties are studied such as Schwarzan derivative equation, soliton solutions and so on.(2). The Painleve property of (2+1) dimensional BB equation is studied.Its Painleve integrability is proved and its soliton solutions are obtained. The Darboux Backlund transformation is found, and bilinear transformation is obtained by means of the Painleve analysis. The solitons of BB equation are obtained by the bilinear transformation. Interestingly, we find that the solutions obtained by the both methods are the same to a certian extent.(3). Soliton fusion or fission phenomenon of 2soliton solutions are found by graphics analysis. The emergence of fusion phenomenon is revealed by the asymptotic analysis.