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We experimentally generate two-dimensional Jones-Roberts solitons in a three-dimensional atomic Bose-Einstein condensate by imprinting a triangular phase pattern. By monitoring their dynamics we observe that this kind of solitary waves are…

We present a family of exact solutions of one-dimensional nonlinear Schr\"odinger equation, which describe the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive…

Other Condensed Matter · Physics 2009-11-11 Z. X. Liang , Z. D. Zhang , W. M. Liu

We investigate the dynamics of the localized nonlinear matter wave in spin-1 Bose-Einstein condensates with trapping potentials and nonlinearities dependent on time and space. We solve the three coupled Gross-Pitaevskii equation by…

Pattern Formation and Solitons · Physics 2017-02-16 Yu-Qin Yao , Wei Han , Ji Li , Hui-lan Wu , Wu-Ming Liu

The Gross-Pitaevskii equation, or more generally the nonlinear Schr\"odinger equation, models the Bose-Einstein condensates in a macroscopic gaseous superfluid wave-matter state in ultra-cold temperature. We provide analytical study of the…

Analysis of PDEs · Mathematics 2019-08-07 Luigi Galati , Shijun Zheng

A double pair plasma system containing cold inertial positive and negative ions, and inertialess super-thermal electrons and positrons is considered. The standard nonlinear Schr\"{o}dinger equation is derived by using the reductive…

Plasma Physics · Physics 2019-04-16 N. K. Tamanna , N. A. Chowdhury , A. Mannan , A. A. Mamun

The analytical nonautonomous rogons are reported for the inhomogeneous nonlinear Schr\"odinger equation with variable coefficients in terms of rational-like functions by using the similarity transformation and direct ansatz. These obtained…

Exactly Solvable and Integrable Systems · Physics 2015-05-20 Zhenya Yan

Topological solitons are relevant in several areas of physics [1]. Recently, these configurations have been investigated in contexts as diverse as hydrodynamics [2], Bose-Einstein condensates [3], ferromagnetism [4], knotted light [5] and…

Mathematical Physics · Physics 2016-10-12 Miguel Bezares , Érico Goulart , Gonzalo Palomera , Daniel J. Pons , Enrique G. Reyes

Consider the cubic nonlinear Schr\"odinger equation set on a d-dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent. We show that, on average, the evolution of the moduli of the…

Analysis of PDEs · Mathematics 2021-03-15 Tristan Buckmaster , Pierre Germain , Zaher Hani , Jalal Shatah

We study spatial optical solitons in a one-dimensional nonlinear photonic crystal created by an array of thin-film nonlinear waveguides, the so-called Dirac-comb nonlinear lattice. We analyze modulational instability of the extended…

Pattern Formation and Solitons · Physics 2007-05-23 Andrey A. Sukhorukov , Yuri S. Kivshar

Nonlinear systems can exhibit a rich set of dynamics that are inherently sensitive to their initial conditions. One such example is modulational instability, which is believed to be one of the most prevalent instabilities in nature. By…

Quantum Gases · Physics 2017-05-02 Jason H. V. Nguyen , De Luo , Randall G. Hulet

We study the dynamics of solitons under the action of one-dimensional quasiperiodic lattice potentials, fractional diffraction, and nonlinearity. The formation and stability of the solitons is investigated in the framework of the fractional…

Pattern Formation and Solitons · Physics 2025-04-11 Eduard Pavlyshynets , Luca Salasnich , Boris A. Malomed , Alexander Yakimenko

We introduce a complete analytical and numerical study of the modulational instability process in a system governed by a canonical nonlinear Schr\"odinger equation involving local, arbitrary nonlinear responses to the applied field. In…

Pattern Formation and Solitons · Physics 2015-01-08 David Novoa , Daniele Tommasini , José A. Nóvoa-López

Spontaneous pattern formation in a variety of spatially extended nonlinear system always occurs through a modulation instability: homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the…

Pattern Formation and Solitons · Physics 2015-08-25 S. Kumar , R. Herrero , M. Botey , K. Staliunas

We study the nonlinear localized modes in two-component Bose-Einstein condensates with parity-time-symmetric Scarf-II potential, which can be described by the coupled Gross-Pitaevskii equations. Firstly, we investigate the linear stability…

Mathematical Physics · Physics 2023-06-06 Jia-Rui Zhang , Xia Wang

We investigate the integrability of generalized nonautonomous nonlinear Schr\"odinger (NLS) equations governing the dynamics of the single- and double-component Bose-Einstein condensates (BECs). The integrability conditions obtained…

Atomic and Molecular Clusters · Physics 2010-11-08 Cai-Ying Ding , Fang Zhang , Dun Zhao , Hong-Gang Luo , W. -M. Liu

We consider the following nonlinear Schr\"{o}dinger equation with derivative: \begin{equation} iu_t =-u_{xx} -i |u|^{2}u_x -b|u|^4u , \quad (t,x) \in \mathbb{R}\times\mathbb{R}, \ b \in\mathbb{R}. \end{equation} If $b=0$, this equation is a…

Analysis of PDEs · Mathematics 2022-08-09 Noriyoshi Fukaya , Masayuki Hayashi

We discuss the (in)stability of solitary waves for a quasi-linear Schr{\"o}dinger equation. The equation contains a quasi-linear term, responsible for a saturation effect, as well as a power nonlinearity. For different exponents of the…

Analysis of PDEs · Mathematics 2025-09-03 Meriem Bahhi , Jonas Lampart , Christian Klein , Simona Rota Nodari

We report the computational discovery of complex, topologically charged, and spectrally stable states in three-dimensional multi-component nonlinear wave systems of nonlinear Schr{\"o}dinger type. While our computations relate to…

Pattern Formation and Solitons · Physics 2023-02-01 N. Boullé , I. Newell , P. E. Farrell , P. G. Kevrekidis

Quasiparticle approach to dynamics of dark solitons is applied to the case of ring solitons. It is shown that the energy conservation law provides the effective equations of motion of ring dark solitons for general form of the nonlinear…

Pattern Formation and Solitons · Physics 2010-10-05 A. M. Kamchatnov , S. V. Korneev

The effective dynamics of solitons for the generalized nonlinear Schr\"odinger equation in a random potential is rigorously studied. It is shown that when the external potential varies slowly in space compared to the size of the soliton,…

Mathematical Physics · Physics 2008-06-17 Walid K. Abou Salem , Catherine Sulem