Study On Solitary Solutions And Periodic Solutions Of Nonlinear Boussinesq Equation And Its Coupled Equations

Nonlinear dynamics problems are widely applied in various fields of naturalsciences and social sciences. To research them makes the nonlinear science shinemore vitality. Most nonlinear problems can be described by nonlinear evolutionequations. Therefore, seeking the solutions of nonlinear evolution equations is oftheoretical and practical significance. The solitary wave solutions are one kind of thesolutions of nonlinear evolution equations with important applications in manysubjects.In this dissertation, we apply an expanded Jacobi elliptic function expansionmethod to obtain solutions of nonlinear Boussinesq equation and its coupledequations. The main results are obtained as follows:Firstly, an expanded Jacobi elliptic function expansion method is applied toconstruct the new travelling solutions for nonlinear Boussinesq equation. Thesolutions obtained by this method include solitary solutions, periodic solutions in theform of Jacobi elliptic function solutions. In the limit case, the corresponding solitarywave solutions and the triangle function solutions are derived.Secondly, an expanded Jacobi elliptic function expansion method is applied toconstruct the new travelling solutions for two variant Boussinesq equations. Moreabundant solutions are obtained. It is shown that this method is an effective tool forsolving the variant Boussinesq equation.Finally, an expanded Jacobi elliptic function expansion method is applied toconstruct the new solutions for the coupled Schr dinger-Boussinesq equations. Weobtain a number of periodic wave solutions expressed by various Jacobi ellipticfunctions. The results replenish and perfect previous known ones.