Symmetry Analysis And Exact Solutions Of Fractional Breaking Soliton Equation

As an important part of nonlinear dynamics,soliton is widely used in various disciplines.After long-term exploration and experiments of many scholars at home and abroad,many methods of solving nonlinear partial differential equations in soliton theory have been developed greatly.Among them,fractional order or fractal calculus is widely studied by scholars as the current hot spot.Firstly,a new local order breaking soliton equation is derived by simplifying the linear spectral problem of the local order non-isospectral self-dual Yang-Mills equation.Specifically,the linear spectral problem is reduced to(2 + 1)-dimensional local order zero curvature equation by variable transformation.Based on the simplified local fractional zero curvature equation,the fractional breaking soliton equation is constructed by the undetermined coefficient method.Then,the symmetry of the(2 + 1)dimensional partial order breaking soliton equation is studied by using the definition of the Lie group.By using the symmetry reduction,the(2+ 1)-dimensional partial order breaking soliton equation is simplified into a class of(1 +1)-dimensional non linear equation.Finally,by solving one of the reduced equations,we find some new exact solutions for the(2 + 1)-dimensional partial order breaking soliton equation,and give the conservation laws of the(2 + 1)-dimensional partial order breaking soliton equation.In this paper,it is shown that a local order model can be obtained by generalizing the existing generation method of integer order breaking soliton equation.The soliton dynamics evolution of this local order equation is worth studying.