Optical collapse is a fascinating research topic. The propagation of intense laser beams in a
transparent medium is usually modeled by the two-dimensional nonlinear Schrödinger …

We analyze self-focusing and singularity formation in the nonlinear Schrödinger equation
(NLS) with high-order dispersion i\psi_t±Δ^qψ+|ψ|^2σψ=0, in the isotropic mixed-dispersion …

This paper considers the effect of Anderson acceleration (AA) on the convergence order of
nonlinear solvers in fixed point form xk+ 1= g (xk), that are looking for a fixed point x∗ of g …

The standard explanation for multiple filamentation of laser beams is that breakup of
cylindrical symmetry is initiated by noise in the input beam. In this study we propose an …

This work introduces, analyzes, and demonstrates an efficient and theoretically sound
filtering strategy to ensure the condition of the least-squares problem solved at each iteration …

In many problems, one wishes to solve the Helmholtz equation with variable coefficients
within the Laplacian-like term and use a high order accurate method (eg, fourth order …

Although intensive research of the influence of ground motion duration on structural
cumulative damage has been carried out, the influence of dynamic responses in …

The well-posedness of a nonlinear Helmholtz equation with an impedance boundary
condition is established for high frequencies in two and three dimensions. Stability estimates …

In this chapter, we discuss computational problems, solution methods, and their efficient
implementation. We describe different approaches to writing algorithms to solve a particular …

The nonlinear Helmholtz equation (NLH) models the propagation of electromagnetic waves
in Kerr media, and describes a range of important phenomena in nonlinear optics and in …