After a transformation, the inverse scattering transform for the derivative nonlinear Schr6dinger （DNLS） equation is developed in terms of squared spectral parameter. Following this approach, we obtain the orthogona...After a transformation, the inverse scattering transform for the derivative nonlinear Schr6dinger （DNLS） equation is developed in terms of squared spectral parameter. Following this approach, we obtain the orthogonality and completeness relations of free Jost solutions, which is impossibly constructed with usual spectral parameter in the previous works. With the help these relations, the Zakharov-Shabat equations as well as Marchenko equations of IST are derived in the standard way.展开更多
It is shown that the space-periodic solutions of the equation of a ferromagnetic chain(the socalled Landau-Lifshits equation)can be obtained by solving the Lax pair equations of the non-linear Schrodinger equation wit...It is shown that the space-periodic solutions of the equation of a ferromagnetic chain(the socalled Landau-Lifshits equation)can be obtained by solving the Lax pair equations of the non-linear Schrodinger equation with the space-periodic potential in the case of the zero spectrum parameter.As an example,the one-band solution is found by this method.展开更多
Disregarding that the locations of poles of the transmission coefficient must be in the upper half-plane of k that is given by the usual inverse scattering method,solutions of the nonlinear Schrodinger equation are fo...Disregarding that the locations of poles of the transmission coefficient must be in the upper half-plane of k that is given by the usual inverse scattering method,solutions of the nonlinear Schrodinger equation are found from the Gelfand-Levitan-Marchenko equation by taking the poles at arbitrary places in the complex k-plane.By using the technique of matrix calculation,a simple method is given for directly verifying the solutions in satisfying the nonlinear Schrodinger equation.As an example,new solutions corresponding to the locations of two poles in pairs symmetrically about the origin of the complex k-plane is given and its regularity is shown.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 10705022, and the Postdoctoral Fund of Huazhong University of Science and Technology （0101011110）.
文摘After a transformation, the inverse scattering transform for the derivative nonlinear Schr6dinger （DNLS） equation is developed in terms of squared spectral parameter. Following this approach, we obtain the orthogonality and completeness relations of free Jost solutions, which is impossibly constructed with usual spectral parameter in the previous works. With the help these relations, the Zakharov-Shabat equations as well as Marchenko equations of IST are derived in the standard way.
基金supported in part by the Science Fund of the Chinese Academy of Science.
文摘It is shown that the space-periodic solutions of the equation of a ferromagnetic chain(the socalled Landau-Lifshits equation)can be obtained by solving the Lax pair equations of the non-linear Schrodinger equation with the space-periodic potential in the case of the zero spectrum parameter.As an example,the one-band solution is found by this method.
基金supported by the Chinese National Fund for Natural Science Researches。
文摘Disregarding that the locations of poles of the transmission coefficient must be in the upper half-plane of k that is given by the usual inverse scattering method,solutions of the nonlinear Schrodinger equation are found from the Gelfand-Levitan-Marchenko equation by taking the poles at arbitrary places in the complex k-plane.By using the technique of matrix calculation,a simple method is given for directly verifying the solutions in satisfying the nonlinear Schrodinger equation.As an example,new solutions corresponding to the locations of two poles in pairs symmetrically about the origin of the complex k-plane is given and its regularity is shown.
