Lump And Its Interaction With Soliton Solutions Of Higher Order Nonlinear Partial Differential Equations

Wave is the main cause of many ship and marine platform accidents every year.In these destructive waves,soliton wave,lump wave and rouge wave have received extensive attention due to their local structures.Lump wave is local in all directions of space,which has attracted more and more researchers' interest in recent years.It is found that there are some interesting phenomena in the interaction between lump waves and solitons.When lump wave interacts with single soliton,the phenomenon of fission and fusion occurs between the two kinds of waves.More importantly,the soliton wave pair can excite a rogue wave when lump wave interacts with a soliton pair.As we all know,rogue wave with the characteristics:“appear from nowhere and disappear without a trace”,has the relatively concentrated energy,which is strong destructive to human society.It is significant to study the interaction between lump wave and soliton for the study of rouge wave.In this thesis,we study lump wave and its interaction with soliton solutions of the(2+1)-dimensional Date-Jimbo-Kashiwara-Miwa(DJKM)equation and the nonintegrable(2+1)-dimensional extended higher-order Broer-Kaup(BK)system by using the Hirota's bilinear direct method.This thesis consists of four chapters.In the first chapter,we mainly introduce the research background and methods of this subject.In the second chapter,we transform the(2+1)-dimensional DJKM equation into fourlinear form through the variable transformation,and obtain the lump solutions by assuming the solution as the rational function.When the solution is supposed as the linear combination of rational and exponential functions,we get the interaction solution between one lump and one soliton,which exhibits fission and fusion phenomena.Finally,by taking the solution as the form of combination of the rational function and two exponential functions,we derive the interaction solution between one lump and one soliton pair.The type of solution describes that lump arises from a soliton and disappears into another soliton,which gives rise to the two-dimensional rouge wave's phenomenon.In the third chapter,we propose a nonintegrable(2+1)-dimensional extended higherorder BK system.Firstly,the lump solution of the nonintegrable(2+1)-dimensional extended higher-order BK system is presented by taking the solution as the rational function directly.Then we construct the interaction solution between one lump and one soliton by assuming the solution as the form of the linear combination of rational and exponential functions.In this interaction solution,two kinds of local waves exhibit two phenomena: fission and fusion.Besides,we get the interaction solution between one lump and two soliton by taking solution as the linear combination of rational function and two exponential functions.It is shown that one lump emerges from a soliton and is absorbed by another soliton,this process generates the rouge wave's phenomenon.Finally,the periodic lump wave solution is obtained by constructing the solution as the linear combination of exponential and triangle functions.In the last chapter,we summarize and discuss this thesis,and outlook on the future research of lump wave and its interaction with other local waves.