| With the development of nonlinear science, nonlinear equations are applied widely in physics, mechanics, geoscience, life sciences, applied mathematics, and engineering. Finding the solutions of nonlinear evolution equations is an interesting work to physical scientists and mathematicians. In this paper we obtained many solutions of several important nonlinear partial differential equations and studied characters of equations.(1) We obtained the Backlund transformation of (3+1)-dimensional KP equation, and derived the multi-soliton solution and lump solution. We also investigated three solitons interaction for (2+1)-dimensional equation, and find, under certain conditions, that the maximum amplitude can reach 9 times of initial interaction solitons for three solitons that with same amplitudes.(2) By using the Function Expansion Method we got some solutions for Burgers equation, KdV equation and KdV-Burgers equation with variable coefficients. Many exact solutions including solitary wave, singularity traveling wave solutions and other kind of solutions are obtained.(3) A class of exact solitary wave solutions for the (3+1)-dimensional Zakharov-Kuznetsov (ZK) equation which contains three arbitrary variable coefficients are obtained by using the WTC method. The results indicate that the coefficients of the equation will not change the wave amplitude, but change the wave velocity.(4) The generalized solutions are obtained for a class of KdV equations, including the damping KdV equations, the cylindrical KdV equations and spherical KdV equations. The results indicate that the amplitude and the velocity of the waves change as time changes.(5) We solved the Burgers equation by using the homotopy analysis method and obtained its kink solitary wave solutions. The results indicate that this method is valid to find the solitary wave solutions for a class of nonlinear evolution equations.
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