The present status and development of strong-field nano-optics, an emerging field of
nonlinear optics, is discussed. A nonperturbative regime of light-matter interactions is …

This review article revisits and outlines the perfectly matched layer (PML) method and its
various formulations developed over the past 25 years for the numerical modeling and …

In this paper, we begin with the nonlinear Schrödinger/Gross–Pitaevskii equation
(NLSE/GPE) for modeling Bose–Einstein condensation (BEC) and nonlinear optics as well …

This book provides an introduction to some modern computational techniques for
optimization problems governed by partial differential equations (PDEs). The optimization …

The phenomenon of Bose–Einstein condensation is a phase transition originally predicted
by Bose and Einstein in 1924. In particular, it was shown that below a critical temperature T …

We introduce infinite range exterior complex scaling (irECS) which provides for complete
absorption of outgoing flux in numerical solutions of the time-dependent Schrödinger …

One-dimensional fractional anomalous sub-diffusion equations on an unbounded domain
are considered in our work. Beginning with the derivation of the exact artificial boundary …

Gauge invariance was discovered in the development of classical electromagnetism and
was required when the latter was formulated in terms of the scalar and vector potentials. It is …

The problem of highly nonlinear photoemission from a metal surface is considered using
analytical and numerical approaches. Descriptions are found which cover both the weak …

The inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an
effort to benchmark and design approximate exchange‐correlation potentials. The forward …