The current understanding of some important nonlinear collective processes in quantum
plasmas with degenerate electrons is presented. After reviewing the basic properties of …

Dense quantum plasmas are ubiquitous in planetary interiors and in compact astrophysical
objects (eg, the interior of white dwarf stars, in magnetars, etc.), in semiconductors and …

The analysis of singular perturbed differential equations began early in the twentieth
century, when approximate solutions were constructed from asymptotic expansions …

Solving optimization problems subject to constraints given in terms of partial d-ferential
equations (PDEs) with additional constraints on the controls and/or states is one of the most …

Starting with the simplest semiclassical approaches and ending with the description of
complex fully quantum-mechanical methods for quantum transport analysis of state-of-the …

This book primarily concerns quasilinear and semilinear elliptic and parabolic partial
differential equations, inequalities, and systems. The exposition leads the reader through the …

This introductory graduate text is based on a graduate course the author has taught
repeatedly over the last ten years to students in applied mathematics, engineering sciences …

In this survey we consider the development and mathematical analysis of numerical
methods for kinetic partial differential equations. Kinetic equations represent a way of …

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 …

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