The Soliton Solutions Of Several Types Of Local Fractional Nonlinear Partial Differential Equations

As nonlinear partial differential equations are widely used in various disciplines,many calculus problems that cannot be dealt with by the classical Newton-Leibniz calculus have emerged in response to more and more complex actual conditions.Researchers have put forward a variety of new calculus theory.For example,the local fractional derivative proposed to describe some natural phenomena in fractal space has become an excellent tool for solving important problems in the fields of particle physics,wave dynamics,electromagnetics,materials science,acoustics,and electrochemistry.The local fractional calculus is also known as fractal calculus.Based on the Riemann-Liouville fractional derivative,it was first proposed by Kolwankar and Gangal,and it has important applications in physics and engineering.Based on the basic knowledge of the definition and properties of local fractional derivatives,this paper takes several types of local fractional nonlinear partial differential equations as the research object,makes reasonable variable substitutions for the target equation,and uses local fractional Hirota bilinear The method turns the equation into a local fractional bilinear derivative form,and finally uses the unique properties of bilinear derivative and truncation method to obtain its soliton solution.The main work of this paper is as follows:The first part is the introduction,which briefly introduces the origin,development,application,research background and significance of local fractional calculus.The second part is preliminary knowledge,which summarizes the definition,properties and related special functions of local fractional calculus.The classical Hirota bilinear method is extended to the local fractional Hirota bilinear method.The third,fourth,and fifth parts respectively introduce in detail how to apply the local fractional Hirota bilinear method to find the soliton solutions of the local fractional KdV equation and two types of two-dimensional Boussinesq equations,and2+1-dimensional BKP equations.The sixth part summarizes and prospects the content of the full text,and gives some directions for further research.