Related papers: Exterior complex scaling as a perfect absorber in …
We establish the existence of positive segregated solutions for competitive nonlinear Schr\"odinger systems in the presence of an external trapping potential, which have the property that each component is obtained from the previous one by…
We propose an adaptive approach in picking the wave-number parameter of absorbing boundary conditions for Schr\"{o}dinger-type equations. Based on the Gabor transform which captures local frequency information in the vicinity of artificial…
Discrete de Rham (DDR) methods provide non-conforming but compatible approximations of the continuous de Rham complex on general polytopal meshes. Owing to the non-conformity, several challenges arise in the analysis of these methods. In…
To solve the time-dependent Schr\"odinger equation in spatially inhomogeneous pulses of electromagnetic radiation, we propose an iterative semi-classical complex trajectory approach. In numerical applications, we validate this method…
In this paper, we propose a family of time-stepping schemes for approximating general nonlinear Schr\"odinger equations. The proposed schemes all satisfy both mass conservation and energy conservation. Truncation and dispersion error…
We consider the integrable family of symmetric boundary-driven interacting particle systems that arise from the non-compact XXX Heisenberg model in one dimension with open boundaries. In contrast to the well-known symmetric exclusion…
We consider the cubic nonlinear Schr\"odinger equation with an exceptional potential. We obtain a sharp time decay for the global in time solution and we get the large time asymptotic profile of small solutions. We prove the existence of…
In this work, we present an efficient approach to solve nonlinear high-contrast multiscale diffusion problems. We incorporate the explicit-implicit-null (EIN) method to separate the nonlinear term into a linear term and a damping term, and…
Absorption of light is directly associated with dissipative processes in a material. In suitably tailored resonators, a specific level of dissipation can support coherent perfect absorption, the time-reversed analogue of lasing, which…
We present and analyze fully discrete Nystr\"om methods for the solution of three classes of well conditioned boundary integral equations for the solution of two dimensional scattering problems by homogeneous dielectric scatterers.…
We relax the usual diagonal constraint on the matrix representation of the eigenvalue wave equation by allowing it to be tridiagonal. This results in a larger solution space that incorporates an exact analytic solution for the non-central…
We consider the inverse problem for time-dependent semilinear transport equations. We show that time-independent coefficients of both the linear (absorption or scattering coefficients) and nonlinear terms can be uniquely determined, in a…
Phenomenological scaling arguments suggest the existence of universal amplitudes in the finite-size scaling of certain correlation lengths in strongly anisotropic or dynamical phase transitions. For equilibrium systems, provided that…
In this paper, we design a truly exact and optimal perfect absorbing layer (PAL) for domain truncation of the two-dimensional Helmholtz equation in an unbounded domain with bounded scatterers. This technique is based on a complex…
We present an implicit-explicit (IMEX) scheme for semilinear wave equations with strong damping. By treating the nonlinear, nonstiff term explicitly and the linear, stiff part implicitly, we obtain a method which is not only unconditionally…
We use the optimized trigonometric finite basis method to find energy eigenvalues and eigenfunctions of the time-independent Schrodinger equation with high accuracy. We apply this method to the quartic anharmonic oscillator and the harmonic…
Through temporal shaping of the excitation signal, the complex-frequency scattering zeros of a lossless structure can be accessed, enabling a storage-release mechanism referred to as coherent virtual absorption. Practical demonstrations of…
We examine conditions for finite-time collapse of the solutions of the higher-order nonlinear Schr\"odinger (NLS) equation incorporating third-order dispersion, self-steepening, linear and nonlinear gain and loss, and Raman scattering; this…
We consider fully discrete numerical schemes for a downscaling data assimilation algorithm aimed at approximating the velocity field of the 2D Navier-Stokes equations corresponding to given coarse mesh observational measurements. The time…
We consider the inverse problem of fitting atmospheric dispersion parameters based on time-resolved back-scattered differential absorption Lidar (DIAL) measurements. The obvious advantage of light-based remote sensing modalities is their…