Dromion structures in the(2+1)-dimensional nonlinear Schrödinger equation with a parity-time-symmetric potential

Abstract

Please cite this article as: Y.-Q. Li, W.-J. Liu, P. Wong, L.-G. Huang, N. Pan, Dromion structures in the (2 + 1)-dimensional nonlinear Schrödinger equation with a parity-time-symmetric potential, Appl. Math. Lett. (2015), http://dx. AbstractIn this paper, the (2+1)-dimensional variable-coefficient nonlinear Schrödinger equation with a paritytime-symmetric potential UP T (r, ϕ) is investigated. With the separation of variables, the solutions for that equation are obtained. Via the obtained solutions, some dromion structures are derived with corresponding parameters, and the influences of them (especial parity-time-symmetry) are analyzed and studied. Results show that the parity-time-symmetric potential plays an important role for obtaining dromion structures.

Rogue waves of the nonlocal Davey–Stewartson I equation

“…We have also derived the nonlocal NLS equation and its higher-order flow by the algebraic splitting method [28,29]. Physical systems with multidimensional PT symmetry have also been extensively investigated, and several interesting analytical results have been obtained, which include: two dimensional spatial solitons in PT symmetric potentials [30], two-dimensional spatial solitons in highly nonlocal nonlinear media [31], and three-dimensional optical vertex and necklace solitons in highly nonlocal nonlinear media [32]; see also [33][34][35]. Recently, by employing a certain reduction of a multidimensional integrable system, Fokas extended the nonlocal NLS equation (1) into two-spatial dimensional space, and introduced the following new integrable nonlocal Davey-Stewartson (DS) equation [36] :…”

Breathers and rogue waves for a third order nonlocal partial differential equation by a bilinear transformation

“…A popular method to derive the rogue waves theoretically is the Darboux transformation [14], but Eqs. (6)(7)(8)(9)(10) have demonstrated that the bilinear method is a feasible scheme in computing breathers (and subsequently rogue waves). This alternative is especially valuable as most soliton systems possess bilinear forms.…”

“…A general framework for coupled nonlinear Schrödinger equations can be formulated [9]. Finally, this whole idea can be extended to equations with two or more spatial variables [10].…”