Soliton Solutions For A Generalized Nonlocal Discrete Hirota Equation And Relevant Studies

Along with more than 40 years of development,the theory of soliton has great achievement both in theory and physical application.In many natural science disciplines,important issues closely related to soliton theory,such as fluid mechanics,Plasma physics,nonlinear optics,classical field theory and quantum field theory.With the improvement of soliton research,the promotion and research of soliton equations has attracted the attention of scholars.Especially the nonlocal integrable equations related to the PT symmetry in the popular research field of modern physics.In this paper,a form of non-local discrete Hirota equation is proposed.The Hirota bilinear method is used to solve the N-soliton solution of the equation.In addition,by setting the form of the solution,discrete breather solution and solton-plane wave solution are given by a special set of the parameters.In addition,soliton system with so(3,R)also promotes the development of soliton theory,and a large number of new equations are derived from it.In this paper,some analysis of the new equations are done,and a part of the solution of the specific equation is given.The main work of this paper consists of two parts:Propose a form of the non-local discrete Hirota equation,and solve the N-soliton solution by using the bilinear method.Introducing a plane-background wave to obtain a new bilinear equation,then set a special solution for the new equation,finally,determine the undetermined coefficient to obtain the discrete breather solution and solton-plane wave solution;The second part mainly introduces the so(3,R)system and solves the specific equations in the real domain.Finally,we discusses the idea of the properties of the so(3,R)equation family.The main work of this paper consists of three parts:Propose a form of the non-local discrete Hirota equation,and solve the N-soliton solution by using the bilinear method;Introducing a plane-background wave to obtain a new bilinear equation,then set a special solution for the new equation,finally,determine the undetermined coefficient to obtain the discrete breather solution and solton-plane wave solution;In the third part,for the generalization of the soliton equation,the theoretical analysis and comparison of the solution of the specific equation in the real domain and the original equation are carried out.Chapter.2 Uses the potential transformation to transform the equation into a bilinear form.Then,through the method of small parameter perturbation expansion,the 1-,2-soliton solution of the equation is obtained.And since the coefficient relationship is complicated,a set of marks is introduced to represent the system simply.Finally,the specific N-soliton solution could written by the comparison of the 1-,2-soliton solution Then,discusses the breather solution of the nonlocal discrete Hirota equation.Firstly,the plane background wave is introduced,then a new bilinear form of the equation is obtained by a variable transformation.By setting the function form,the discrete breather solution and solton-plane wave solution are obtained by substituting the function form into the bilinear equationChapter.3 It is mainly for the solution of the so(3,R)equation family proposed by Professor Ma.It is well known that the study of nonlinear equations is often related to its practical application and background in physi cs,optics or other fields,so the new equation family is conducive to our deeper understanding of natural science.The bilinear method is not directly applicable to solving the so(3,R)equation,so we first make a transformation to make it easy to solve directly.Then,a partial solution of the first set of equations is given in the real domain.