Interaction Behaviors Of Solitoffs: Fssion, Fusion, Reconnection And Annihilation

In the past thirty years,nonlinear science is substantially studied and widely ap-plied in natural sciences such as biology,chemistry,mathematics,communication andalmost all the physical branches like condensed matters,field theory,low temperaturephysics,hydrodynamics,plasma physics,optics and so on,where a large amount of non-linear systems emerge.Therefore, a lot of question are naturally asked: How to solvethese nonlinear partial differential equations which describe the nonlinear systems. Inthe past, many methods have been established and developed to solve the nonlinearsystems especially those integrable ones, for instance,the inverse scattering transfor-mation(the extension of the Fourier transformation to the nonlinear systems),separationapproach,functional variable separation approach,derivative dependent functional vari-able separation approach and so on. To solve nonlinear systems especially to obtainreduction solutions there are two fundamental methods,CK's direct method and clas-sical or nonclassical Lie group approach. The former solves PDEs algebraically andthe latter is based on the group theory. It is believed that traditional reduction methodsare quite perfect and some standard types of reductions solutions are exhausted.Recently, the direct searching for the solution of the nonliear partial differen-tial equations has become more and more popular. For instance,the special functionexpansion method and the extended special function expansion method.If we choosethe special function as tanh,sech,sn or cn repectively,then the corresponding specialfunction expansion method are called the tanh-function expansion method,the sech-function expansion method,the Jacobi-function expansion method.The paper is mainly focus its research on the following . The interactions ofsolitoffs are investigated. Besides the known solitoff fission and fusion interactions,two new types of solitoff interactions are reported in the second chapter, named the...