69 citations · 115 across the 9 of their papers we have counts for
8 papers · 1 filter
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…
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…
Uniform Bose-Einstein Condensates as Kovaton solutions of the Gross-Pitaevskii Equation through a Reverse-Engineered Potential
Fred Cooper, Avinash Khare, John F. Dawson +2
In this work, we consider a ``reverse-engineering'' approach to construct confining potentials that support exact, constant density kovaton solutions to the classical Gross-Pitaevs…
Rogue Waves in Ultracold Bosonic Seas
E. G. Charalampidis, J. Cuevas-Maraver, D. J. Frantzeskakis +1
In this work, we numerically consider the initial value problem for nonlinear Schrödinger (NLS) type models arising in the physics of ultracold boson gases, with generic Gaussian w…
Lattice Three-Dimensional Skyrmions Revisited
E. G. Charalampidis, T. A. Ioannidou, P. G. Kevrekidis
In the continuum a skyrmion is a topological nontrivial map between Riemannian manifolds, and a stationary point of a particular energy functional. This paper describes lattice ana…