Related papers: Inverse scattering transform and multi-solition so…
The inverse scattering transform for the focusing nonlinear Schrodinger equation is presented for a general class of initial conditions whose asymptotic behavior at infinity consists of counterpropagating waves. The formulation takes into…
In this paper, the inverse scattering transform for the integrable discrete nonlocal PT symmetric nonlinear Schr\"odinger equation with nonzero boundary conditions is presented. According to the two different signs of symmetry reduction and…
We study the initial-value problem for the nonlinear Schr\"odinger equation. Application of the inverse scattering transform method involves solving direct and inverse scattering problems for the Zakharov-Shabat system with complex…
Inverse scattering transform method of the heat equation is developed for a special subclass of potentials nondecaying at space infinity---perturbations of the one-soliton potential by means of decaying two-dimensional functions. Extended…
Matrix generalization of the inverse scattering method is developed to solve the multicomponent nonlinear Schr\"odinger equation with nonvanishing boundary conditions. It is shown that the initial value problem can be solved exactly. The…
In 2013 a new nonlocal symmetry reduction of the well-known AKNS scattering problem was found; it was shown to give rise to a new nonlocal $PT$ symmetric and integrable Hamiltonian nonlinear Schr\"{o}dinger (NLS) equation. Subsequently, the…
The multichannel scattering problem for the stationary Schr\"{o}dinger equation on a line with different thresholds at both infinities is investigated. The analytical structure of the Jost solutions and of the transition matrix relating the…
We study the direct and inverse scattering problem for the one-dimensional Schr\"odinger equation with steplike potentials. We give necessary and sufficient conditions for the scattering data to correspond to a potential with prescribed…
This paper is devoted to the study of the defocusing nonlinear Schr\"{o}dinger equation with a self-consistent source and nonzero boundary conditions by the method of the inverse scattering problem. In cases where the source consists of a…
Within the framework of the Riemann-Hilbert problem, the theory of inverse scattering transform is established for the defocusing nonlinear Schr\"{o}dinger equation with local and nonlocal nonlinearities (which originates from the…
We study an inverse source scattering problem for the Schr\"odinger equation with a quadratic nonlinearity. In general, uniqueness of inverse source problems can not be guaranteed at a fixed energy. Therefore, additional information is…
The purpose of the present paper is to develop the inverse scattering transform for the nonlocal semi-discrete nonlinear Schrodinger equation (known as Ablowitz-Ladik equation) with PT-symmetry. This includes: the eigenfunctions (Jost…
A system of linear integral equations is presented, which is the analog of the system of Marchenko integral equations, to solve the inverse scattering problem for the linear system associated with the derivative NLS equations. The…
The challenge of solving the initial value problem for the coupled Lakshmanan Porsezian Daniel equation, while considering nonzero boundary conditions at infinity, is addressed through the development of a suitable inverse scattering…
A generalized inverse scattering method has been applied to the linear problem associated with the coupled higher order nonlinear schr\"odinger equation to obtain it's $N$-soliton solution. An infinite number of conserved quantities have…
The inverse scattering transform is extended to investigate the Tzitz\'{e}ica equation. A set of sectionally analytic eigenfunctions and auxiliary eigenfunctions are introduced. We note that in this procedure, the auxiliary eigenfunctions…
In this paper, we explore the integrable fractional derivative nonlinear Schr\"odinger (fDNLS) equation by using the inverse scattering transform. Firstly, we start from the recursion operator and obtain a formal fDNLS equation. Then the…
The Nonstationary Schr\"{o}dinger equation with potential being a perturbation of a generic one-dimensional potential by means of a decaying two-dimensional function is considered here in the framework of the extended resolvent approach.…
We present a simple approach for finding $N$-soliton solution and the corresponding Jost solutions of the derivative nonlinear Scr\"{o}dinger equation with nonvanishing boundary conditions. Soliton perturbation theory based on the inverse…
In this paper, we study an inverse scattering problem associated with the time-harmonic Schr\"odinger equation where both the potential and the source terms are unknown. The source term is assumed to be a generalised Gaussian random…