Apply Hirota Bilinear To Solve The Rogue Waves Of Some Coupling Equations

Solution of the equation is the emphases and difficulties of nonlinear partial differen-tial equation is studied, and the theory of soliton is also a research hotspot. This paper mainly studies the two types of integrable equation:the coupling Schrodinger - KdV equation and the KP - â…¡ equation with self-consistent sources by using the Hirota bilinear method. It is often used for directly solving soliton solution and rational solution of nonlinear partial differential equations. According to different types of equation, we used the different ways to analyze equation. First of all by introducing new functions, potential equation transformation will be converted to bilinear form. And we expand the new function disturbance, and make parameters to take limiting. The second way converts bilinear equation to Ï„ function and the form of a strange wave solution of the original equation is obtained. It will change the shape of rogue wave under the different parameters.Chapter 2. On the basis of the bilinear form of the coupling Schrodinger - KdV equation, the rogue wave solution of the coupling Schrodinger-KdV equation is derived. Firstly, a new variate is applied, and the equation is transformed into double linear equation. Then the new function is unfolded with some parameters. The rogue wave is obtained through taking the limit of the parameters.Chapter 3. Research is mainly focused on the rogue wave solutions of the KP - â…¡ equation with self-consistent sources. On the basis of the double linear equation, the original equation is transformed into equivalent equation containing new variables by variable substitution. The rational solutions are obtained by using the Ï„ function. Then, the rogue wave solutions of the equation can be derived. The fundamental rogue waves and second order rogue waves to blame collisions are made a detailed analysis of the dynamics.