Soliton,Breather And Rogue Wave Solutions Of ML-Ⅳ Equation

Many phenomena that exist objectively in nature are nonlinear.Today,with the rapid and precise development of science and technology,production practice has also put forward higher and higher requirements for solving nonlinear partial differential equations.Through the efforts of generations of scientific researchers,a relatively complete theoretical system has been established for solving nonlinear partial differential equations.The soliton in the soliton theory is a kind of special wave that keeps its shape and speed unchanged during the propagation process and does not lose energy.It can not only reflect a class of stable natural phenomena,but also the characteristics of a large class of nonlinear interactions.Homogeneous equilibrium method,Jacobi elliptic function expansion method,bilinear method,etc.They have greatly expanded the scope of explicit solutions for nonlinear partial differential equations.This article mainly investigated the(2+1)-dimensional multi-coupling Myrzakulov-Lakshmanan-IV( ML-Ⅳ)equation.This nonlinear equation is studied in depth from the soliton solution,breather solution and the high-order rogue wave solution by using the Darboux transformation method,combined with symbolic calculation and professional mathematical software.And the 3D image is drawn,so that we can easily analyze the shape,nature and meaning of the solution.The exact solution of the ML-Ⅳ equation studied in this paper are presented as follows:1.The one-fold and N-fold generalized DT are constructed for the(2+1)-dimensional ML-Ⅳ equation using the Lax pair,and they are proved theoretically.The dynamic propagation characteristics of the single-soliton solution under the background of the initial zero solution is discussed by using professional software to draw and adjust the parameters.Then the collision of the double-soliton solution are simulated and the dynamic change characteristics of the limit analysis are given.We explained the elastic collision mechanism in detail.2.We investigated two types of breather solutions of the ML-Ⅳ equation under the background of plane waves solution firstly.Secondly,by using the breather-to-soliton state conversion mechanism,the images are drawn and its dynamic propagation characteristics are discussed,various nonlinear excitations such as multi-peak solitons,periodic solitons,Wshaped solitons and antidark solitons have been obtained.And their excitation conditions have been summarized and then the properties and characteristics of the solutions can be analyzed.3.The high-order rogue wave solutions of the ML-Ⅳ equation is obtained under a non-zero background,and the dynamic propagation characteristics of the rogue wave solutions are discussed by using symbolic calculation and professional software to adjust the parameters.And many interesting rogue wave structures are obtained.There is also a better understanding of rogue wave: it appears suddenly and vanishes without foundation.