(2 + 1) -dimensional Calogero Bogoyavlenskii - Schiff Equation Is Reduced And Its New Exact Solutions Of Symmetry

Classical Lie group method, modified CK direct method, Undetermined coefficient method is given for nonlinear partial differential equation reduction three similar resolve the most effective method.This paper using the three meth-ods study (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (CBS) equation, get the equation of Lie symmetry and reduction equation then obtained a lot of the exact solution.It shows the three methods of the same and different,the main works are as follows:In chapter1, Describes the theoretical background of group theory thought and the present situation and the main content of this paper studies.In chapter2, Using the method of lie groups seeking (2+1)-dimensional CBS system and its the invariant solution of symmetrical Lie, use the invariant solution of the system reduce into ordinary differential equation.In chapter3, We mainly discussed the use of the modified of CK direct method for solving (2+1)-dimensional CBS equation has been reduced equa-tion and the exact solution. And set up between the new and old solution of the relationship.This method shows that don’t need any group of theory thoughts can get all the symmetry reduction.In chapter4,This chapter of undetermined coefficient method is used to solve the (2+1)-dimensional CBS equation of symmetry, first discussed the equation should satisfy the conditions, and by using the method of undetermined coef-ficients equation reduce into ordinary differential equation,And get some new exact solutions of the equation.