83 citations · 592 across the 50 of their papers we have counts for
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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…
On the proximity of Ablowitz-Ladik and discrete Nonlinear Schrödinger models: A theoretical and numerical study of Kuznetsov-Ma solutions
Madison L. Lytle, Efstathios G. Charalampidis, Dionyssios Mantzavinos +3
In this work, we investigate the formation of time-periodic solutions with a non-zero background that emulate rogue waves, known as Kuzentsov-Ma (KM) breathers, in physically relev…
Solitary waves in the coupled nonlinear massive Thirring as well as coupled Soler models with arbitrary nonlinearity
Avinash Khare, Fred Cooper, John F. Dawson +2
Motivated by the recent introduction of an integrable coupled massive Thirring model by Basu-Mallick et al, we introduce a new coupled Soler model. Further we generalize both the c…
Learning Traveling Solitary Waves Using Separable Gaussian Neural Networks
Siyuan Xing, Efstathios G. Charalampidis
In this paper, we apply a machine-learning approach to learn traveling solitary waves across various families of partial differential equations (PDEs). Our approach integrates a no…
Exact trapped -soliton solutions of the nonlinear Schrödinger equation using the inverse problem method
Fred Cooper, Avinash Khare, John F. Dawson +2
In this work, we show the application of the ``inverse problem'' method to construct exact trapped soliton-like solutions of the nonlinear Schrödinger or Gross-Pitaevskii equat…