Exact Solutions Of The Nonlinear Alice-Bob System

With the depth study of actual physical problems,the nonlinear effects have been extended to nonlocal situations,that is,nonlocal nonlinear systems are established.Subsequently,the symmetric(PT symmetric)nonlinear system satisfying parity(P)and time reversal(T)has caused extensive research,such as in the fields of nonlinear optics,complex crystals,quantum dynamics,Bose-Einstein condensation and electromagnetics.In recent years,a nonlocal Alice-Bob(AB)system is established to describe the physical related events in two or more places based on the general AB-BA equivalence principle.In the process of establishing the AB model,not only the parity(P)and time-reversal(T),but also the charge-conjugation(C),the parity with shifted parity(Ps)and delayed time reversal(Td)are considered.Based on the application of symmetry theory,this paper starts research from the exact solution of nonlocal nonlinear equations.The specific work is as follows:In the first part,a brief history of finding solitary waves and solitons is outlined and the development of nonlinear wave theory,and then introduced the AB system and several basic methods for studying soliton solutions in this paper.The research arrangement of the dissertation is given in the end of this chapter.In the second part,we study the abundant symmetry breaking solutions of nonlocal AliceBob Benjamin-Ono(AB-BO)system,the nonlocal AB-BO system is induced via the parity and time reversal symmetry reduction.By introducing an extended Backlund transformation,the symmetry breaking soliton,breather and lump solutions for this system are obtained through the derived Hirota bilinear form.By taking suitable constants in the involved ansatz functions,abundant fascinating symmetry breaking structures of the related explicit solutions are shown.In the third part,based on the Hirota bilinear method and symbolic computation,abundant exact solutions,including lump,lump-soliton and breather solutions,are computed for the coupled Alice-Bob system of the Hirota-Satsuma-Ito(HSI)equation in(2+1)-dimensions.The three-dimensional figures of these solutions are presented,which illustrate the characteristics of these solutions.The last part is the summary and prospect of this paper.