Study On The Interaction Of Multi-lumps,The Formation Mechanism And Manipulation Of The Rogue Waves

Waves pose a great threat to the safety of ships,oil platforms,ports and so on.It is the main cause of a large number accidents involved ships and ocean platforms every year.The wave height can be up to twenty or thirty meters on the ocean,it can cause great destructive damage to the engineering buildings.The large amplitude waves also can cause great threat to the security of the submarine and underwater vehicles.More and more attentions have been paid to these destructive waves,such as rogue waves,solitary waves,lump and so on.Rogue wave is a disaster on the ocean,it is difficult to predict when it will happen.But the dynamics of optical rogue waves can be controlled in nonlinear optical fiber with dispersion,nonlinearity and gain(loss)managements.By properly choosing the distributed coefficients,various controllable sceneries have been realized,including the periodically recurrence,suppression or even annihilation and sustainment of optical rogue waves.Moreover,the study on optical rogue wave may have potential values for the design of fiber optic amplifier and the generation of super bright light optical pulses.Above all,it's important to explore the dynamics of the rogue waves,lump and their interaction.We mainly focus on two kinds of equations: the Kadomtsev–Petviashvili 1(KP)equation which is used to model the waves of shallow water and nonlinear Schr?dinger(NLS)equation with variable coefficients which is used to model optical rogue waves in nonlinear media.We mainly study on the lump solution and their interaction within KP1 equation,the rogue wave solutions and their control within NLS equation.The main work and results of the thesis are outlined as follows.1)The interactions of multi-lumps within the Kadomtsev-Petviashvili 1(KP1)equation are studied analytically and numerically.The dependence of stationary multi-lump structures on free parameters is discussed.The interactions of lumps with each other,as well as the interactions of the solitary wave are studied.Propose a mechanism to the formation of rogue waves–the interaction between lumps.At last the ring soliton and lump solution of the c KP equation are constructed.2)The generation of symmetric and asymmetric lumps by a straight and oblique three-dimensional bottom topography is numerically investigated using the forced Kadomtsev-Petviashvili 1(f KP1)equation.The wave structures and propagation properties are studied for several forcings,such as the orientation and volume of the different bottom topographies.At last rogue waves are generated by multi bottom topographies.3)Similarity transformation is used to construct exact high order rogue wave solutions of(1+1)-dimensional NLS equation,Then,the manipulation of the multi rogue waves in optical fibre within the(1+1)-dimensional NLS equation is discussed.4)Similarity transformation is used to construct exact line optical rogue wave solutions of(2+1)-dimensional NLS equation with varying coefficients.Transmission control of line optical rogue waves in two-dimension graded-index waveguide within the(2+1)-dimensional NLS equation is discussed.