Similarity Transformation And Some Exact Solutions Of A Generalized Variable-coefcient (2+1)-dimensional Breaking Soliton Equation

Most phenomena in the real world cannot fully describe just rely on the linear model, so the scientists begin to pay attention to the nonlinear model.The nonlinear model play an important role in the biological, physical, chemical, communication, economy etc..And the nonlinear differential equation is an important representation of nonlinear model.It has very important application in multiple disciplines to know the law of nature and social development, promote the useing of the nature. Soliton, chaos and fractal is the most popular field of nonlinear models.Soliton is a self-reinforcing solitary wave (a wave pulse) which maintains its shape while it travels at constant speed aftera cancellation, especially in the study of optical communication, soliton equation has very important significance.Many powerful and efficient methods for searching for exact solutions of nonlinear par-tial differential equations was constructed by a group of scientists, such as inverse scattering transformation[1]、Backlund transformation [2]、CK’s direct method[3,4]、bilinear method and multilinear method [5-7]、classical and non-classical Lie group approaches [8,9]、truncated Painleve expansion[10-12],etc.on the basis of the symmetry group direct method and symbolic computation, a similarity transformation are constructed for a generalized variable coefficient (2+1)-dimensional break-ing soliton equation. From this similarity transformation, the variable-coefficients equation are reduced to the corresponding constant-coefficients equation and the finite symmetry transfor-mation groups for the constant coefficient case can be derived. Some exact solutions of the constant coefficient (2+1)-dimensional breaking soliton equation are derived by the projective Riccati equations method. Thus, the corresponding general solutions can also be constructed through the similarity transformation.