134 citations
13 papers
CAO: Curvature-Adaptive Optimization via Periodic Low-Rank Hessian Sketching
Wenzhang Du
First-order optimizers are reliable but slow in sharp, anisotropic regions. We study a curvature-adaptive method that periodically sketches a low-rank Hessian subspace via Hessian-…
The interaction of Airy waves and solitons in the three-wave system
Thawatchai Mayteevarunyoo, Boris A. Malomed
We employ the generic three-wave system, with the interaction between two components of the fundamental-frequency (FF) wave and second-harmonic (SH) one, to consider coll…
Two-dimensional solitons generated by the downconversion of Airy waves
Thawatchai Mayteevarunyoo, Boris A. Malomed
Conversion of truncated Airy waves (AWs) carried by the second-harmonic (SH) component into axisymmetric solitons is considered in the 2D system with the quadratic nonlinea…
Generation of \c{hi}2 solitons from the Airy wave through the parametric instability
Thawatchai Mayteevarunyoo, Boris A. Malomed
Spontaneous creation of solitons in quadratic media by the downconversion, i.e., parametric instability against the generation of fundamental-frequency excitations, from the trunca…
Gap solitons attached to a gapless layer
Thawatchai Mayteevarunyoo, Boris A. Malomed
We consider linear and nonlinear modes pinned to a grating-free (gapless) layer placed between two symmetric or asymmetric semi-infinite Bragg gratings (BGs), with a possible phase…
A solvable model for solitons pinned to a PT-symmetric dipole
Thawatchai Mayteevarunyoo, Boris A. Malomed, Athikom Reoksabutr
We introduce the simplest one-dimensional nonlinear model with the parity-time (PT) symmetry, which makes it possible to find exact analytical solutions for localized modes ("solit…