Related papers: Inverse scattering transform for the Kundu-Eckhaus…
The semiclassical limit of the focusing Nonlinear (cubic) Schr\" odinger Equation (NLS) corresponds to the singularly perturbed Zakharov Shabat (ZS) system that defines the direct and inverse scattering transforms (IST). In this paper, we…
We consider the inhomogeneous nonlinear Schr\"odinger equation $$ i u_t +\Delta u+|x|^{-b}|u|^\alpha u = 0, $$ where $\frac{4-2b}{N}<\alpha<\frac{4-2b}{N-2}$ (when $N=2$, $\frac{4-2b}{N}<\alpha<\infty$) and $0<b<\min\{N/3,1\}$. For a radial…
This paper develops the numerical inverse scattering transform (NIST) framework for the coupled modified Korteweg-de Vries (mKdV) equation based on its associated Riemann-Hilbert problem. The coupled system gives rise to a $3\times3$…
We consider the inverse scattering problem at fixed and sufficiently large energy for the nonrelativistic and relativistic Newton equation in $\R^n$, $n \ge 2$, with a smooth and short range electromagnetic field $(V,B)$. Using results of…
In this study, we explore multiple higher-order pole solutions in spinor Bose--Einstein condensates. These solutions are associated with different pairs of higher-order poles of the transmission coefficient in the inverse scattering…
We present a method to compute dispersive shock wave solutions of the Korteweg-de Vries equation that emerge from initial data with step-like boundary conditions at infinity. We derive two different Riemann-Hilbert problems associated with…
We develop a Riemann-Hilbert approach to the inverse scattering transform method for the short pulse (SP) equation $u_{xt}=u+\frac{1}{6}(u^3)_{xx}$ with zero boundary conditions (as $|x|\to\infty$). This approach is directly applied to the…
A new approach to the inverse-scattering technique of Alekseev is presented which permits real-pole soliton solutions of the Ernst equations to be considered. This is achieved by adopting distinct real poles in the scattering matrix and its…
We study the Cauchy problem for the (2+1) integrable nonlinear Schr\"odinger equation by the inverse scattering transform (IST) method. This Cauchy problem with given initial data and boundary data at infinity is reduced by IST to the…
The inverse quantum scattering problem for the perturbed Bessel equation is considered. A direct and practical method for solving the problem is proposed. It allows one to reduce the inverse problem to a system of linear algebraic…
This work focuses on three-component defocusing Kundu-Eckhaus equation, which serves as a significant coupled model for describing complex wave propagation in nonlinear optical fibers. By employing binary Darboux transformation based on 4x4…
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…
In this paper, the nonlocal reverse space-time derivative nonlinear Schr\"odinger equation under nonzero boundary conditions is investigated using the Riemann-Hilbert (RH) approach. The direct scattering problem focuses on the analyticity,…
Integrable Kondo impurities in two cases of the one-dimensional $t-J$ model are studied by means of the boundary ${\bf Z}_2$-graded quantum inverse scattering method. The boundary $K$ matrices depending on the local magnetic moments of the…
The inverse scattering transform is developed to solve the Maxwell-Bloch system of equations that describes two-level systems with inhomogeneous broadening, in the case of optical pulses that do not vanish at infinity in the future. The…
In this work we consider the inverse elastic scattering problem by an inclusion in two dimensions. The elastic inclusion is placed in an isotropic homogeneous elastic medium. The inverse problem, using the third Betti's formula (direct…
In this paper, we develop the numerical inverse scattering transform (NIST) for solving the derivative nonlinear Schrodinger (DNLS) equation. The key technique involves formulating a Riemann-Hilbert problem (RHP) that is associated with the…
We consider the use of rational basis functions to compute the scattering and inverse scattering transforms associated with the AKNS system. The proposed numerical forward scattering transform computes the solution of the AKNS system that…
We consider the inverse problem of reconstructing the scattering and absorption coefficients using boundary measurements for a time dependent radiative transfer equation (RTE). As the measurement is mostly polluted by errors, both…
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…