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Related papers: Benjamin-Ono equation: Rogue waves, generalized br…

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We study nonlinear internal gravity waves (IGWs) in the atmosphere. The reductive perturbation method is used to derive a system of two-dimensional nonlinear equations for the envelope of velocity stream function and the mean flow. In the…

Pattern Formation and Solitons · Physics 2023-07-04 Volodymyr M. Lashkin , Oleg K. Cheremnykh

We analyze vector localized solutions of two-component Bose-Einstein condensates (BECs) with variable nonlinearity parameter and external trap potential through similarity transformation technique which transforms the two coupled…

Pattern Formation and Solitons · Physics 2016-04-06 K. Manikandan , P. Muruganandam , M. Senthilvelan , M. Lakshmanan

We investigate the Zeno dynamics of the optical rogue waves. Considering their usage in modeling rogue wave dynamics, we analyze the Zeno dynamics of the Akhmediev breathers, Peregrine and Akhmediev-Peregrine soliton solutions of the…

Quantum Physics · Physics 2018-01-17 Cihan Bayindir , Fatih Ozaydin

We report the experimental observation of vector extensions of Peregrine solitons in highly particle-imbalanced, pairwise immiscible three-component repulsive Bose-Einstein condensates (BECs). The possibility of an effectively attractive…

Quantum Gases · Physics 2025-10-30 G. A. Bougas , G. C. Katsimiga , S. Mossman , P. Engels , P. G. Kevrekidis , S. I. Mistakidis

In many physical contexts, notably including deep water waves, modulation instability in one space dimension is often studied using the nonlinear Schr\"odinger equation. The principal solutions of interest are solitons and breathers which…

Fluid Dynamics · Physics 2022-06-13 Montri Maleewong , Roger Grimshaw

Based on the bilinear operator and symbol calculation, some lump solutions are presented, rationally localized in all directions in the space, to a reduced (3+1)-dimensional KP equation. The lump solutions all contain six parameters, four…

Exactly Solvable and Integrable Systems · Physics 2017-05-24 Xiaoen Zhang , Yong Chen , Xiaoyan Tang

In this paper, the generalized Darboux transformation is established to the AB system, which mainly describes marginally unstable baroclinic wave packets in geophysical fluids and ultra-short pulses in nonlinear optics. We find a unified…

Mathematical Physics · Physics 2013-12-24 Xin Wang , Yuqi Li , Yong Chen

Modulational instability has been used to explain the formation of breather and rogue waves qualitatively. In this paper, we show modulational instability can be used to explain the structure of them in a quantitative way. We develop a…

Exactly Solvable and Integrable Systems · Physics 2017-04-04 Liming Ling , Li-Chen Zhao

Rogue waves are known to be much more common on jet currents. A possible explanation was put forward in [ [V. Shrira and A. Slunyaev, Nonlinear dynamics of trapped waves on jet currents and rogue waves, Phys. Rev. E 89, 041002, 2014]]: for…

Fluid Dynamics · Physics 2023-10-12 A. V. Slunyaev , V. I. Shrira

Algebraic soliton interactions with a periodic or quasi-periodic random force are investigated using the Benjamin-Ono equation. The random force is modeled as a Fourier series with a finite number of modes and random phases uniformly…

Pattern Formation and Solitons · Physics 2024-09-09 Marcelo V. Flamarion , Efim Pelinovsky , Ekaterina Didenkulova

We analytically and numerically study three-component rogue waves (RWs) in spin-1 Bose-Einstein condensates with Raman-induced spin-orbit coupling (SOC). Using the multiscale perturbative method, we obtain approximate analytical solutions…

Quantum Gases · Physics 2024-09-16 Jun-Tao He , Hui-Jun Li , Ji Lin , Boris A. Malomed

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 construct infinitely many real-valued, time-periodic breather solutions of power-type nonlinear wave equations. These solutions are obtained from critical points of a dual functional and they are weakly localized in space. Our abstract…

Analysis of PDEs · Mathematics 2021-08-11 Rainer Mandel , Dominic Scheider

Within the (2 + 1)-dimensional Korteweg-de Vries equation framework, new bilinear Backlund transformation and Lax pair are presented based on the binary Bell polynomials and gauge transformation. By introducing an arbitrary function, a…

Exactly Solvable and Integrable Systems · Physics 2020-12-29 Yulei Cao , Peng-Yan Hu , Yi Cheng , Jingsong He

This study aims to explore the complex interactions between an internal solitary wave and an external force using the Benjamin-Ono equation as the theoretical framework. The investigation encompasses both asymptotic and numerical…

Fluid Dynamics · Physics 2023-07-04 Marcelo V. Flamarion , Efim Pelinovsky

General high-order rogue waves of the NLS-Boussinesq equation are obtained by the KP-hierarchy reduction theory. These rogue waves are expressed with the determinants, whose entries are all algebraic forms. It is found that the fundamental…

Exactly Solvable and Integrable Systems · Physics 2017-10-25 Xiaoen Zhang , Yong Chen

In this paper, we systematically investigate the intricate dynamics of the breather-to-soliton transitions and nonlinear wave interactions for the higher-order generalized Gerdjikov-Ivanov equation. The transition conditions of the…

Pattern Formation and Solitons · Physics 2025-08-13 Yanan Wang , Minghe Zhang

General high-order rogue wave solutions for the (1+1)-dimensional Yajima-Oikawa (YO) system are derived by using Hirota's bilinear method and the KP-hierarchy reduction technique. These rogue wave solutions are presented in terms of…

Exactly Solvable and Integrable Systems · Physics 2018-08-29 Junchao Chen , Yong Chen , Bao-Feng Feng , Ken-ichi Maruno , Yasuhiro Ohta

This is a study of the Euler equations for free surface water waves in the case of varying bathymetry, considering the problem in the shallow water scaling regime. In the case of rapidly varying periodic bottom boundaries this is a problem…

Analysis of PDEs · Mathematics 2016-01-20 Walter Craig , David Lannes , Catherine Sulem

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