170 citations · 232 across the 8 of their papers we have counts for
8 papers
Breather gas fission from elliptic potentials in self-focusing media
Gino Biondini, Gennady A. El, Xu-Dan Luo +2
We present an analytical model of integrable turbulence in the focusing nonlinear Schrödinger (fNLS) equation, generated by a one-parameter family of finite-band elliptic potential…
Soliton-mean field interaction in Korteweg-de Vries dispersive hydrodynamics
Mark J. Ablowitz, Justin T. Cole, Gennady A. El +2
The propagation of localized solitons in the presence of large-scale waves is a fundamental problem, both physically and mathematically, with applications in fluid dynamics, nonlin…
Elliptic finite-band potentials of a non-self-adjoint Dirac operator
Gino Biondini, Xu-Dan Luo, Jeffrey Oregero +1
We present an explicit two-parameter family of finite-band Jacobi elliptic potentials for a non-self-adjoint Dirac operator which connects two previously known limiting cases in wh…
Instability intervals of the Whittaker-Hill operator
Xu-Dan Luo
The Hill operator admits a band gap structure. As a special case, like the Mathieu operator, one has only open gaps, however, the instability intervals of the Whittaker-Hill operat…
Solitons, the Korteweg-de Vries equation with step boundary values and pseudo-embedded eigenvalues
Mark J. Ablowitz, Xu-Dan Luo, Justin T. Cole
The Korteweg-deVries (KdV) equation with step boundary conditions is considered, with an emphasis on soliton dynamics. When one or more initial solitons are of sufficient size they…
General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions
Bao-Feng Feng, Xu-Dan Luo, Mark J. Ablowitz +1
General soliton solutions to a nonlocal nonlinear Schrödinger (NLS) equation with PT-symmetry for both zero and nonzero boundary conditions {are considered} via the combination of…
Inverse scattering transform for the nonlocal reverse space-time Sine-Gordon, Sinh-Gordon and nonlinear Schrödinger equations with nonzero boundary conditions
Mark J. Ablowitz, Bao-Feng Feng, Xu-Dan Luo +1
The reverse space-time (RST) Sine-Gordon, Sinh-Gordon and nonlinear Schrödinger equations were recently introduced and shown to be integrable infinite-dimensional dynamical systems…
Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions
Mark J. Ablowitz, Xu-Dan Luo, Ziad H. Musslimani
In 2013 a new nonlocal symmetry reduction of the well-known AKNS scattering problem was found; it was shown to give rise to a new nonlocal symmetric and integrable Hamiltonian…