104 citations · 285 across the 17 of their papers we have counts for
17 papers
Blowup of Multi-Peaked Waveforms in the Two-Dimensional Nonlinear Schroedinger Model
S. Jon Chapman, M. Kavousanakis, E. G. Charalampidis +2
In the present work, we explore the self-focusing and resulting collapse of two-dimensional waveforms involving multiple pulses in a nonlinear Schroedinger equation with a general…
Multi-hump Collapsing Solutions in the Nonlinear Schr{ö}dinger Problem: Existence, Stability and Dynamics
Jon S. Chapman, Mihalis Kavousanakis, Efstathios G. Charalampidis +2
In the present work we examine multi-hump solutions of the nonlinear Schr{ö}dinger equation in the blowup regime of the one-dimensional model with power law nonlinearity, bearing a…
Global Bifurcations in a Damped-Driven Diatomic Granular Crystal
D. Pozharskiy, I. G. Kevrekidis, P. G. Kevrekidis
We revisit here the dynamics of an engineered dimer granular crystal under an external periodic drive in the presence of dissipation. Earlier findings included a saddle-node bifurc…
Self-similar blow-up solutions in the generalized Korteweg-de Vries equation: Spectral analysis, normal form and asymptotics
S. Jon Chapman, M. Kavousanakis, E. G. Charalampidis +2
In the present work we revisit the problem of the generalized Korteweg-de Vries equation parametrically, as a function of the relevant nonlinearity exponent, to examine the emergen…
Equation-Free Computations as DDDAS Protocols for Bifurcation Studies: A Granular Chain Example
M. O. Williams, Y. M. Psarellis, D. Pozharskiy +5
This chapter discusses the development and implementation of algorithms based on Equation-Free/Dynamic Data Driven Applications Systems (EF/DDDAS) protocols for the computer-assist…
Revisiting Diffusion: Self-similar Solutions and the Decay in Initial and Initial-Boundary Value Problems
P. G. Kevrekidis, M. O. Williams, D. Mantzavinos +3
The diffusion equation is a universal and standard textbook model for partial differential equations (PDEs). In this work, we revisit its solutions, seeking, in particular, self-si…