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We theoretically investigate the solitary waves and their switching dynamics in a $\mathcal{PT}$-symmetric directional fiber coupler, exhibiting Kerr nonlinearity, by developing a variational analysis. We analyze the fundamental switching…

Optics · Physics 2022-06-22 Ambaresh Sahoo , Amarendra K. Sarma

In this work, we study the dynamics of rogue waves in the partially $\cal{PT}$-symmetric nonlocal Davey-Stewartson(DS) systems. Using the Darboux transformation method, general rogue waves in the partially $\cal{PT}$-symmetric nonlocal DS…

Mathematical Physics · Physics 2017-10-20 Bo Yang , Yong Chen

We present a multi-parameter family of rational solutions to the complex Korteweg-de Vries(KdV) equations. This family of solutions includes particular cases with high-amplitude peaks at the centre, as well as a multitude of cases in which…

Exactly Solvable and Integrable Systems · Physics 2020-09-22 Matthew Crabb , Nail Akhmediev

We discuss the behavior of solitary wave solutions of the nonlinear Schr{\"o}dinger equation (NLSE) as they interact with complex potentials, using a four parameter variational approximation based on a dissipation functional formulation of…

Pattern Formation and Solitons · Physics 2016-09-21 Franz G. Mertens , Fred Cooper , Edward Arevalo , Avinash Khare , Avadh Saxena , A. R. Bishop

In the present work, we explore the possibility of developing rogue waves as exact solutions of some nonlinear dispersive equations, such as the nonlinear Schr\"odinger equation, but also, in a similar vein, the Hirota, Davey-Stewartson,…

Pattern Formation and Solitons · Physics 2019-02-15 C. B. Ward , P. G. Kevrekidis

Since the parity-time-(PT-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with PT-symmetric potentials have been investigated. However, previous studies of PT-symmetric waves were…

Pattern Formation and Solitons · Physics 2017-05-29 Yong Chen , Zhenya Yan , Dumitru Mihalache , Boris A. Malomed

We analytically study rogue-wave (RW) solutions and rational solitons of an integrable fifth-order nonlinear Schr\"odinger (FONLS) equation with three free parameters. It includes, as particular cases, the usual NLS, Hirota, and…

Pattern Formation and Solitons · Physics 2017-03-31 Yunqing Yang , Zhenya Yan , Boris A. Malomed

We report and discuss analytical solutions of the vector nonlinear Schr\"odinger equation that describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and dark-dark rogue waves. The link between…

Exactly Solvable and Integrable Systems · Physics 2014-07-23 Fabio Baronio , Matteo Conforti , Antonio Degasperis , Sara Lombardo , Miguel Onorato , Stefan Wabnitz

By rearrangements of waveguide arrays with gain and losses one can simulate transformations among parity-time (PT-) symmetric systems not affecting their pure real linear spectra. Subject to such transformations, however, the nonlinear…

Pattern Formation and Solitons · Physics 2012-05-29 D. A. Zezyulin , V. V. Konotop

We systematically construct a distinct class of complex potentials including parity-time ($\cal PT$) symmetric potentials for the stationary Schr\"odinger equation by using the soliton and periodic solutions of the four integrable real…

Exactly Solvable and Integrable Systems · Physics 2017-10-11 K. Tamilselvan , T. Kanna , Avinash Khare

We measure evolution of spectra, spatial correlation functions and probability density functions (PDFs) of waves appearance for a set of one-dimensional NLS-like equations of focusing type, namely for the classical integrable Nonlinear…

Optics · Physics 2015-03-20 Dmitry Agafontsev , Vladimir Zakharov

Starting from the von Neumann-Maxwell equations for the Wigner quasi-probability distribution and for the self-consistent electric field, the quantum analog of the classical single-wave model has been derived. The linear stability of the…

Plasma Physics · Physics 2011-10-24 Stephan I. Tzenov , Kiril B. Marinov

We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schr\"{o}dinger equations. Based on the generalized Darboux transformation and formal series method, we obtain the high-order rogue wave solution without the…

Pattern Formation and Solitons · Physics 2016-05-31 Li-Chen Zhao , Boling Guo , Liming Ling

General higher order rogue waves of a vector nonlinear Schrodinger equation (Manakov system) are derived using a Darboux-dressing transformation with an asymptotic expansion method. The Nth order semi-rational solutions containing 3N free…

Exactly Solvable and Integrable Systems · Physics 2014-04-14 Gui Mu , Zhenyun Qin , Roger Grimshaw

It is known that multidimensional complex potentials obeying $\mathcal{PT}$-symmetry may possess all real spectra and continuous families of solitons. Recently it was shown that for multi-dimensional systems these features can persist when…

Pattern Formation and Solitons · Physics 2017-01-04 J. D'Ambroise , P. G. Kevrekidis

General higher-order breather and rogue wave (RW) solutions to the two-component long wave--short wave resonance interaction (2-LSRI) model are derived via the bilinear Kadomtsev-Petviashvili hierarchy reduction method and are given in…

Exactly Solvable and Integrable Systems · Physics 2022-07-18 Jiguang Rao , Boris A. Malomed , Dumitru Mihalache , Jingsong He

Nonlinear wave propagation in parity-time ($\mathcal{PT}$) symmetric localized potentials is investigated analytically near a phase-transition point where a pair of real eigenvalues of the potential coalesce and bifurcate into the complex…

Pattern Formation and Solitons · Physics 2016-06-29 Sean Nixon , Jianke Yang

We investigate, by direct numerical simulations, the dynamics of the damped and forced nonlinear Schr\"odinger (NLS) equation in the presence of a time periodic forcing and for certain parametric regimes. It is thus revealed, that the…

Pattern Formation and Solitons · Physics 2021-05-19 Sevastos Diamantidis , Theodoros P. Horikis , Nikos I. Karachalios

In this work, we consider the dynamics of vector rogue waves and dark-bright solitons in two-component nonlinear Schr\"odinger equations with various physically motivated time-dependent nonlinearity coefficients, as well as…

Pattern Formation and Solitons · Physics 2014-10-23 R. B. Mareeswaran , E. G. Charalampidis , T. Kanna , P. G. Kevrekidis , D. J. Frantzeskakis

The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schr\"odinger equation (NLS) provides a mechanism. A Peregrine wave solution can be obtained by taking the…

Fluid Dynamics · Physics 2015-11-03 Y. Charles Li