The Exact Solutions For The (3+1)-dimensional BKP Equation

This degree thesis mainly involving research for the (3+1)-dimensional generalization of the BKP equation and two new forms of the (3+1)-dimensional BKP equation. Based on the Hirota’s bilinear method, the Wronskian technique and the Pfaffian properties, Wronskian and Grammian solutions have been established for the (3+1)-dimensional generalization of the BKP equation. Wronskian formulation is obtained for each new forms of the (3+1)-dimensional BKP equation by the Wronskian technique and Bell-polynomial. A set of sufficient conditions consisting of systems of linear partial differential equations with free parameters is presented. The resulting Wronskian formulations can yield rational solutions, solitons, negatons and positons by solving the linear conditions.The first chapter mainly introduces the background, significance of the soliton theory.The second chapter introduces some related concepts and properties in the paper, such as Hirota operator and properties, Wronskian formulation definition and properties.The third chapter focus on the Wronskian and Grammian solution for (3+1)-dimensional generalization of the BKP equation.The fourth chapter we mainly consider Wronskian solutions for two new forms of the (3+1)-dimensional BKP equation are investigated, the resulting Wronskian formu-lations can yield rational solutions, solitons, negatons and positons by solving the linear conditions.The fifth chapter Conclusions and remarks.