A ug 2 00 7 Weyl functions , inverse problem and special solutions for the system auxiliary to the nonlinear optics equation
نویسنده
چکیده
A Borg-Marchenko type uniqueness theorem (in terms of the Weyl function) is obtained here for the system auxiliary to the N -wave equation. A procedure to solve inverse problem is used for this purpose. The asymptotic condition on the Weyl function, under which the inverse problem is uniquely solvable, is completed by the new and simple sufficient condition on the potential, granting the fulfillment of this asymptotic condition. The evolution of the Weyl function is discussed and the solution of an initial-boundary value problem for the N -wave equation follows. Explicit solutions of the system are obtained. System with a shifted argument is treated.
منابع مشابه
Fixed point theorems under weakly contractive conditions via auxiliary functions in ordered $G$-metric spaces
We present some fixed point results for a single mapping and a pair of compatible mappings via auxiliary functions which satisfy a generalized weakly contractive condition in partially ordered complete $G$-metric spaces. Some examples are furnished to illustrate the useability of our main results. At the end, an application is presented to the study of exi...
متن کاملOn the GBDT version of the Bäcklund-Darboux transformation and its applications to the linear and nonlinear equations and Weyl theory
A general theorem on the GBDT version of the Bäcklund-Darboux transformation for systems rationally depending on the spectral parameter is treated and its applications to nonlinear equations are given. Explicit solutions of direct and inverse problems for Diractype systems, including systems with singularities, and for the system auxiliary to the N -wave equation are reviewed. New results on ex...
متن کاملOn inverse problem for singular Sturm-Liouville operator with discontinuity conditions
In this study, properties of spectral characteristic are investigated for singular Sturm-Liouville operators in the case where an eigen parameter not only appears in the differential equation but is also linearly contained in the jump conditions. Also Weyl function for considering operator has been defined and the theorems which related to uniqueness of solution of inverse proble...
متن کاملApplications of He’s Variational Principle method and the Kudryashov method to nonlinear time-fractional differential equations
In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...
متن کاملDetermination of a Source Term in an Inverse Heat Conduction Problem by Radial Basis Functions
In this paper, we propose a technique for determining a source term in an inverse heat conduction problem (IHCP) using Radial Basis Functions (RBFs). Because of being very suitable instruments, the RBFs have been applied for solving Partial Dierential Equations (PDEs) by some researchers. In the current study, a stable meshless method will be pro- posed for solving an (I...
متن کامل