Four Nonlinear Partial Differential Equations’ Auxiliary Equation Method And Its Exact Solutions

In the study of computer algebra and differential equation,to con-struction the exact solution of the nonlinear partial differential equation by the differential equation method is a significant problem.In this paper,Based on the existing auxiliary differential equation and combined with G’/G expansion method and general Riccati equation to build new double auxiliary equation method,three auxiliary equation method and extended three auxiliary equation method,we can gain results as follows:(1)the dispersive wave equation; (2)Sharma - Tasso -Olver equation:(3) general variable coefficient KdV-Burgers equation;(4)(2+1)-dimensional of shallow water wave equation.series of new mixing solutions con-tains multiple function such as:complex function solutions,rational function, trigono-metric function,hyperbolic function are obtained.