Investigation On Soliton Solutions Of Coupled Nonlinear Schr?dinger Equations Describing Phenomena Such As Bioenergy Trasfer

It is well known that the nonlinear Schrodinger(NLS)equation is one of the basic models for describing nonlinear phenomena and the soliton is the outcome of a delicate balance between dispersion and nonlinearity for the NLS equation,and it is capable of propagating over long distances without change of shape,amplitude and velocity.The soliton theory has been studied intensively in diverse areas of nonlinear optics,condensed matter physics and biomedical sciences.In recent years,with the development of technology,the investigations of multicomponent nonlinear systems have received much attention.In many practical problems,it is necessary to evolve the standard NLS equation into coupled NLS equations to more accurately depict the specific nonlinear phenomena in the real world.Solitary waves in coupled NLS equations are often called vector solitons and they have more rich phenomena and complex dynamics.The coupled NLS equations can be used to study the energy transfer in ?-helical protein in biomedical field.The soliton is transport carrier of the hydrolysis energy of ATP in protein which causes the vibration of amide-I and distortion of the lattice.Then,under the nonlinear action of protein molecules,the soliton moves along the protein molecular chain and achieves energy transfer.Increasing from a single equation to coupled equations can lead to more complex for getting the exact solution of equations.Therefore,studying the coupled NLS equations deeply and attempts to get exact soliton solutions have profound theoretical significance and wide application value.Based on the results of many researches of the model describing bioenergy transfer in the ?-helical protein,this dissertation is to generalize of the NLS equation from the aspects including by adding the number of couplings,adding the complex terms and variable coefficients.By using the theoretical approach,vector soliton solutions can be obtained and the dynamic properties of soliton solutions are discussed by asymptotic analysis and graphic simulation.The research results in this dissertation are list as follows:1.Investigations on 2-coupled NLS equations model with four-wave mixing terms and linear self-coupling and cross-coupling terms.The periodic soliton solutions were obtained by the developed Hirota bilinear method.We analyzed the relation of the periodic soliton solutions and general vector soliton solutions such as:bright-bright soli-ton solutions,bright-dark(dark-light)soliton solutions and dark-dark soliton solutions.How the four-wave mixing terms and coupled terms influence the propagate property of the solitons was discussed.Via the asymptotic analysis method,we have theoretically proved the mechanism of elastic collisions.2.Investigations on the 2-coupled NLS equations model with arbitrarily time-dependent potential for describing quasi-one-dimensional two-component Bose-Einstein condensates.We obtained the exact nonautonomous superposition N-soliton solutions analytically by the developed Hirota bilinear method.The effect of time-dependent potential on the propagation properties of soliton was analyzed and the interactions between multiple solitons were discussed.3.Investigations on the constant coefficient 3-coupled NLS equations model describ?ing the soliton dynamics in ?-spiral protein.The vector soliton solutions of the model were obtained by reasonable assumptions,including:2-superposition-1-dark solitons,1-bright-2-superposition solitons and periodic solitons.We have analyzed the propagate properties of the soliton solutions and discussed the soliton interactions by asymptotic analysis and graphic simulation.4.Investigations on the variable coefficient 3-coupled NLS model which describing soliton dynamics in the three-spine ?-helical protein with inhomogeneous effect.Consid-ering the coefficients of the model were variable,we obtained the vector periodic soliton solution of the model by using reasonable transformation.When the variable coefficient is a hyperbolic secant function,the propagate properties of solitons were discussed.In addition,we have gotten the two solitons and discussed the interactions as follows:prop-agation without interaction,propagation with periodic interaction and soliton collision.