The Application Of Bell Polynomial In MKP Equation

Soliton theory is one of the most remarkable research directions of nonlinear sciences, and plays an important role in the field of natural science. What’s more, soliton theory is thought to be important to promote the development of nonlinear science theory. In this paper, the research object is isospectral mKP equation and nonisospectral mKP equation. The main content is the application of Bell polynomial in mKP equation.In the first part, we systematically summarize the generation and development of soliton theory and its current research status, as well as the basic knowledge in the paper. The second part is the core part of the paper, we use Bell polynomial to derive the bilinear forms of mKP equation, Backlund transformations and the forms of Lax pairs. First of all, in line with the relationship of Bell polynomials and the bilinear Hirota D-operators, we introduce the bilinear derivative forms and bilinear Backlund transformations of isospectral mKP equation and nonisospectral mKP equation. And then, according to the bilinear Backlund transformation and the relationship of Bell polynomials and Hopf-Cole transformation v=In Ψ, we receive the specific forms of Lax pairs and conjugate Lax pairs for mKP equations and nonisospectral mKP equation.