Analytical Studies On Lump And Rogue Wave Solutions Of Nonlinear Wave Equations

Nonlinear wave equations(NWEs)are hot topics in nonlinear sciences s-ince they can describe large numbers of nonlinear phenomena in mathematic-s,physics,biology,medicine,and so on.As mathematical representations of nonlinear phenomena,NWEs are keys for Mathematicians to investigate the nonlinear problems.In recent decades,nonlinear sciences have achieved rapid development.E-specially,various algorithms have been developed to solve the analytical solu-tions of NWEs.Over the past decade,rogue wave phenomenon has drawn more and more attentions of researchers.As a result,exact rogue wave solutions for NWEs have aroused widespread research interests.In this paper,we focus on the rogue wave and lump solutions of some special NWEs.Also,by virtue of symbolic computation,we simulated the evolution of the solution waves.The main contents of this thesis are as follows:(1)In Chapter 2,we focus on a five-stage Heisenberg equation.Based on Lax pair and the generalized Darboux transformation,we acquire the first-order and second-order rogue wave solutions of the equation.In addition,the effects of equation parameters on the evolution of solution waves are also discussed.(2)By virtue of the generalized Tanh method,we study the BLP equation and the(2+1)-dimensional Breaking Soliton equation in Chapter 3.We obtain non-rational form rogue wave solutions.Evolution of such rogue waves are simulated.(3)In Chapter 4,a constructive algorithm is designed.The potential-YTSF equation and a KP equation with variable coefficients are considered as illus-trative examples to show the efficiency of the algorithm.Rogue wave and lump solutions of the two equations were obtained.