New Traveling Wave Solutions For Two Classes Of Nonlinear Wave Equations

To find solutions for nonlinear partial differential equations is always a frontier topic in the field of mathematical physics.In this thesis,we study two types of nonlinear wave equations: Tzitzeica-Dodd-Bullough equation and Schr （?）dinger-Hirota equation.By applying the polynomial complete discriminant system method,we obtain some new traveling wave solutions for the above two nonliner wave equations.The organizations of this thesis are in following.In the first chapter,we briefly recall the history of searching exact solutions for nonlinear partial differential equations,and introduce the backgrounds,methods and main results of this thesis.In the second chapter,according to the characteristics of the Tzitzeica-Dodd-Bullough equation,we convert it into a solvable ordinary differential equation through some appropriate transformations.By applying the fourth-order complete discriminant system method,then we obtain twelve new traveling wave solutions for Tzitzeica-Dodd-Bullough equation,including four peak solutions and two rational function solutions,a periodic function solution,a triangular function solution,and four Jacobian elliptic function solutions.Furthermore,we draw some typical graphics of traveling wave solutions.The complete discriminant system method is also used to study traveling wave solutions of the double Sinh-Gordon equation.In the third chapter,by applying the third-order polynomial complete discriminant system method,we investigate traveling wave solutions of the Schr （?）dinger-Hirota equation.We obtain new traveling wave solutions for Schr （?）dinger-Hirota equation,including four Jacobian ellipse function solutions,a rational function solution,and a triangular function solution,and draw some graphics of traveling wave solutions.