Study On Solving Higher-dimensional Nonlinear Models And Nonlinear Wave Phenomena In Fluids And Plasmas

Many nonlinear phenomena in the fields of physics can be studied by using the nonlinear evolution equations.Study on solving the nonlinear evolution equations is an important subject in nonlinear science.In this paper,several kinds of the nonlinear evolution equations with higher dimensions in the fields such as fluids and plasmas are analytically studied,and the related nonlinear wave phenomena are analyzed.The main contents of this dissertation are as follows:In chapter 1,we briefly introduce the research background and current status of the nonlinear waves,such as solitons,breathers,rogue waves and lump waves.We illustrate several main research methods used in this paper.Finally,main work and structure arrangement of this paper are introduced.In chapter 2,we investigate a(3+1)-dimensional generalized Kadomtsev-Petviashvili(KP)equation for the long water waves and small-amplitude surface waves with the weak nonlinearity,weak dispersion and weak perturbation in a fluid.Via the Hirota method and extended homoclinic test method,we derive the breather,lump and lump-soliton solutions.We analyse the structural characteristics of the dark breathers and lump waves,as well as the interactions between the bright/dark lump waves and bright/dark solitons.In addition,effects of dispersion,nonlinearity,perturbed and disturbed wave velocity effects on those waves are discussed.In chapter 3,the research objects are two(3+1)-dimensional B-type KP equations,which describe the weakly dispersive waves in fluids.Via the Hirota method,we derive the lump/rogue wave-kink and lump/rogue wave-soliton solutions,respectively.Propagation characteristics of the lump waves and rogue waves are studied by means of figures.Interactions between the lump waves/rogue waves and kinks/solitons are discussed.In chapter 4,we investigate a(3+1)-dimensional generalized B-type KP equation in a fluid.We obtain the breather-soliton,lump wave-soliton and rogue wave-soliton solutions via generalizing the Hirota method and extended homoclinic test method.Interactions between breathers and solitons,dark lump waves and solitons,and rogue waves and solitons are discussed.Effects of the coefficients in the equation on these nonlinear waves are discussed by means of changing the parameters.In chapter 5,we investigate a(3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation for the interfacial waves in a two-layer liquid.Via the KP hierarchy reduction,we derive the rational solutions in the determinant forms and observe the propagation characteristics of the higher-order and multi-lump waves.Via the Hirota method,we obtain the semi-rational solutions and study the interactions between a lump wave/line rogue wave and a soliton.In chapter 6,via the KP hierarchy reduction method,we investigate the lump waves on the non-zero backgrounds for a(3+1)-dimensional generalized variable-coefficient shallow water wave equation in a fluid.The first-order,the higher-order and multi-lump waves on the non-zero backgrounds are observed.Effects of the perturbed and dispersion effects on the lump waves are discussed.In some special cases,line rogue waves appear.In chapter 7,we study a(3+1)-dimensional generalized KP equation in fluid dynamics and plasma physics.Via the KP hierarchy reduction,the higher-order and multi-semi-rational solutions and the higher-order breather solutions in terms of the Gramian are obtained.In addition,we graphically study the solutions.In chapter 8,we summarize the contents of this paper and present the future research directions.