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We discuss the response of both moving and trapped solitary wave solutions of a nonlinear two-component nonlinear Schr\"odinger system in 1+1 dimensions to an anti-$\mathcal{PT}$ external periodic complex potential. The dynamical behavior…

Pattern Formation and Solitons · Physics 2021-05-03 Efstathios G. Charalampidis , Fred Cooper , John F. Dawson , Avinash Khare , Avadh Saxena

In multi-component systems, several rogue waves can be simultaneously excited using simple initial conditions in the form of a plane wave with a small amplitude single-peak perturbation. This is in drastic contrast with the case of…

Pattern Formation and Solitons · Physics 2022-03-09 Chong Liu , Shao-Chun Chen , Xiankun Yao , Nail Akhmediev

In this work, based on the recently proposed (Phys. Rev. Lett. 110 (2013) 064105) continuous nonlocal nonlinear Schr\"odinger system with parity-time symmetric Kerr nonlinearity (PTNLSE), a numerical investigation has been carried out for…

Optics · Physics 2017-11-22 Samit Kumar Gupta

The effect of derivative nonlinearity and parity-time- (PT-) symmetric potentials on the wave propagation dynamics is investigated in the derivative nonlinear Schrodinger equation, where the physically interesting Scarff-II and…

Pattern Formation and Solitons · Physics 2017-04-19 Yong Chen , Zhenya Yan

In the present work, a nonlocal nonlinear Schr\"odinger (NLS) model is studied by means of a recent technique that identifies solutions of partial differential equations, by considering them as fixed points in {\it space-time}. This…

Pattern Formation and Solitons · Physics 2020-03-25 C. B. Ward , P. G. Kevrekidis , T. P. Horikis , D. J. Frantzeskakis

The generation of rogue waves is investigated via a nonlocal nonlinear Schrodinger (NLS) equation. In this system, modulation instability is suppressed and is usually expected that rogue wave formation would also be limited. On the…

Pattern Formation and Solitons · Physics 2017-04-26 Theodoros P. Horikis , Mark J. Ablowitz

We present determinant expressions for vector rogue wave solutions of the Manakov system, a two-component coupled nonlinear Schr\"odinger equation. As special case, we generate a family of exact and non-symmetric rogue wave solutions of the…

Exactly Solvable and Integrable Systems · Physics 2015-06-22 Jingsong He , Lijuan Guo , Yongshuai Zhang , Amin Chabchoub

The focusing Nonlinear Schr\"odinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, the main physical mechanism for the generation of rogue…

Exactly Solvable and Integrable Systems · Physics 2018-05-01 P. G. Grinevich , P. M. Santini

The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schr\"odinger equation (NLS). Within the class of exact NLS…

Fluid Dynamics · Physics 2014-04-01 Amin Chabchoub , Mathias Fink

We explore the existence and dynamical generation of rogue waves (RWs) within a one dimensional quantum droplet bearing environment. RWs are computed by deploying a spacetime fixed point scheme to the relevant extended Gross Pitaevskii…

In this paper, novel rogue wave patterns in the nolocal nonlinear Schr\"odinger equation (NLS) are investigated by means of asymptotic analysis, including heart-pentagon, oval-trangle, and fan-trangle. It is demonstrated that when multiple…

Pattern Formation and Solitons · Physics 2025-03-14 Tingyou Wang , Zhenyun Qin , Gui Mu , Fuzhuang Zheng , Zhijun Qiao

A new exactly solvable (1+1)-dimensional complex nonlinear wave equation exhibiting rich ana- lytic properties has been introduced. A rogue wave (RW), localized in space-time like Peregrine RW solution, though richer due to the presence of…

Pattern Formation and Solitons · Physics 2019-03-27 Abhik Mukherjee , Anjan Kundu

We present trapped solitary wave solutions of a coupled nonlinear Schr\"odinger system in $1$+$1$ dimensions in the presence of an external, supersymmetric and complex $\mathcal{PT}$-symmetric potential. The Schr\"odinger system this work…

Pattern Formation and Solitons · Physics 2020-12-02 Efstathios G. Charalampidis , John F. Dawson , Fred Cooper , Avinash Khare , Avadh Saxena

We construct rogue waves (RWs) in a coupled two-mode system with the self-focusing nonlinearity of the Manakov type (equal SPM and XPM coefficients), spatially modulated coefficients, and a specially designed external potential. The system…

Exactly Solvable and Integrable Systems · Physics 2015-10-23 Wei-Ping Zhong , Milivoj Belić , Boris A. Malomed

We explore the form of rogue wave solutions in a select set of case examples of nonlinear Schr\"odinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe…

Pattern Formation and Solitons · Physics 2014-10-23 J. S. He , E. G. Charalampidis , P. G. Kevrekidis , D. J. Frantzeskakis

In this paper, we investigate the logarithmic nonlinear Schr\"odinger (LNLS) equation with the parity-time (PT)-symmetric harmonic potential, which is an important physical model in many fields such as nuclear physics, quantum optics, magma…

Pattern Formation and Solitons · Physics 2020-12-08 Zijian Zhou , Zhenya Yan

We construct breather and rogue wave solutions of a variable coefficient nonlinear Schr\"odinger equation with an external linear potential. This generalized model describes the nonlinear wave propagation in an inhomogeneous plasma/medium.…

Exactly Solvable and Integrable Systems · Physics 2014-07-14 K. Manikandan , M. Senthilvelan

The derivative nonlinear Schrodinger (DNLS) equation is the canonical model for dynamics of nonlinear waves in plasma physics and optics. We study exact solutions describing rogue waves on the background of periodic standing waves in the…

Exactly Solvable and Integrable Systems · Physics 2021-06-09 Jinbing Chen , Dmitry E. Pelinovsky

We present a comprehensive study of stationary states in a coherent medium with a quadratic or Kerr nonlinearity in the presence of localized potentials in one dimension (1D) for both positive and negative signs of the nonlinear term, as…

Quantum Gases · Physics 2023-11-29 Allison Brattley , Hongyi Huang , Kunal K. Das

A variational technique is established to deal with the Schrodinger equation with parity-time(PT) symmetric Gaussian complex potential. The method is extended to the linear and self-focusing and defocusing nonlinear cases. Some unusual…

Pattern Formation and Solitons · Physics 2012-03-09 Sumei Hu , Guo Liang , Shanyong Cai , Daquan Lu , Qi Guo , Wei Hu