The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type ...The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.展开更多
The Gelfand-Levitan-Marchenko representation is used to analyze the initial-boundary value problem of two-component nonlinear SchrSdinger equation on the haff-line.It has shown that the global relation can be effectiv...The Gelfand-Levitan-Marchenko representation is used to analyze the initial-boundary value problem of two-component nonlinear SchrSdinger equation on the haff-line.It has shown that the global relation can be effectively analyzed by the Geffand-Levitan-Marchenko representation, we also derive expressions for the Dirichlet-to-Neumann map tocharacterize the unknown boundary values.展开更多
In this work,we present a unified transformation method directly by using the inverse scattering method for a generalized derivative nonlinear Schrödinger(DNLS)equation.By establishing a matrix Riemann-Hilbert pr...In this work,we present a unified transformation method directly by using the inverse scattering method for a generalized derivative nonlinear Schrödinger(DNLS)equation.By establishing a matrix Riemann-Hilbert problem and reconstructing potential function q(x,t)from eigenfunctions{Gj(x,t,η)}3/1 in the inverse problem,the initial-boundary value problems for the generalized DNLS equation on the half-line are discussed.Moreover,we also obtain that the spectral functions f(η),s(η),F(η),S(η)are not independent of each other,but meet an important global relation.As applications,the generalized DNLS equation can be reduced to the Kaup-Newell equation and Chen-Lee-Liu equation on the half-line.展开更多
文摘The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.
基金support by NSFC(11671095,11501365)Shanghai Sailing Program supported by Science and Technology Commission of Shanghai Municipality under Grant NO.15YF1408100+1 种基金Shanghai Youth Teacher Assistance program NO.ZZslg15056the Hujiang Foundation of China(B14005)
文摘The Gelfand-Levitan-Marchenko representation is used to analyze the initial-boundary value problem of two-component nonlinear SchrSdinger equation on the haff-line.It has shown that the global relation can be effectively analyzed by the Geffand-Levitan-Marchenko representation, we also derive expressions for the Dirichlet-to-Neumann map tocharacterize the unknown boundary values.
基金This work is supported by the Natural Science Foundation of China(Nos.11601055,11805114 and 11975145)the Natural Science Research Projects of Anhui Province(No.KJ2019A0637)University Excellent Talent Fund of Anhui Province(No.gxyq2019096).
文摘In this work,we present a unified transformation method directly by using the inverse scattering method for a generalized derivative nonlinear Schrödinger(DNLS)equation.By establishing a matrix Riemann-Hilbert problem and reconstructing potential function q(x,t)from eigenfunctions{Gj(x,t,η)}3/1 in the inverse problem,the initial-boundary value problems for the generalized DNLS equation on the half-line are discussed.Moreover,we also obtain that the spectral functions f(η),s(η),F(η),S(η)are not independent of each other,but meet an important global relation.As applications,the generalized DNLS equation can be reduced to the Kaup-Newell equation and Chen-Lee-Liu equation on the half-line.
