Soliton-like Solutions For Some Nonlinear Partial Differential Equations With Variable Coefficients

The modern natural science is changing dramatically, nonlinear science is per-meated with the mathematical science, space science, life sciences and Earth Sciencesand become the important field of contemporary scientific research. there are manymodels can be used by Soliton theory to describe the nonlinear evolution equations,so the analytic solutions (exact solutions) of nonlinear partial diferential equationsbecome an important part the soliton theory. The methods to solve non-linear dif-ferential equations has made many breakthroughs, but the equations with constantcoefcients can only approximate the movement, the nonlinear evolution equationswith variable coefcients are more common. To accurately describe the propertiesof movement, the solutions of nonlinear equations with variable coefcients are veryimportant, because the nonlinear equations with variable coefcients has been moregeneral.In this paper, new exact soliton solutions are constructed on the basis of theexisting theory of soliton and the methods for the solutions of nonlinear partialdiferential equations.In chapter1, the concept of solitons, development, applications and the meth-ods for gaining exact solutions in soliton thoery are outlined. In chapter2, newexact soliton solutions for (3+1)-dimensional Kaolomtsev-Petviashvili equationand fifth Model equation with variable coefcients are obtained by using the Jacobielliptic function expansion method. In chapter3, new exact soliton solutions for(2+1)-dimensional Kaolomtsev-Petviashvili equation are obtained by using sine-Gordon as the assistant equation method. In chapter4, new exact soliton solutionsfor (2+1)-dimensional Painlev′e Integrable Burgers equations are obtained by usingcoupled sub-equations method. In chapter5, new exact soliton solutions for (2+1)-dimensional Nizhnik-Novikov-Vesselov equations are obtained by using the thesub-ODEs method.