176 citations · 564 across the 22 of their papers we have counts for
7 papers · 1 filter
A Nonlinear Journey from Structural Phase Transitions to Quantum Annealing
Mithun Thudiyangal, Panayotis G. Kevrekidis, Avadh Saxena +1
Motivated by an exact mapping between equilibrium properties of a 1-dimensional chain of quantum Ising spins in a transverse field (the transverse field Ising (TFI) model) and a 2-…
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…
Solitary waves in a two-dimensional nonlinear Dirac equation: from discrete to continuum
J. Cuevas-Maraver, P. G. Kevrekidis, A. B. Aceves +1
In the present work, we explore a nonlinear Dirac equation motivated as the continuum limit of a binary waveguide array model. We approach the problem both from a near-continuum pe…
Generalized Dimers and their Stokes-variable Dynamics
H. Xu, P. G. Kevrekidis, A. Saxena
In the present work, we generalize the setting of dimers with potential gain and loss which have been extensively considered recently in -symmetric contexts. We cons…
On Some Classes of mKdV Periodic Solutions
P. G. Kevrekidis, Avinash Khare, A. Saxena +1
We obtain exact periodic solutions of the positive and negative modified Kortweg-de Vries (mKdV) equations. We examine the dynamical stability of these solitary wave lattices throu…
Breather lattice and its stabilization for the modified Korteweg-de Vries equation
P. G. Kevrekidis, Avinash Khare, A. Saxena
We obtain an exact solution for the breather lattice solution of the modified Korteweg-de Vries (MKdV) equation. Numerical simulation of the breather lattice demonstrates its insta…
Scattering of a solitary pulse on a local defect or breather
Panayotis G. Kevrekidis, Boris A. Malomed, H. E. Nistazakis +3
A model is introduced to describe guided propagation of a linear or nonlinear pulse which encounters a localized nonlinear defect, that may be either static or breather-like one (t…