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We study the stability of the standing wave solutions of a Gross-Pitaevskii equation describing Bose-Einstein condensation of dipolar quantum gases and characterize their orbit. As an intermediate step, we consider the corresponding…

Analysis of PDEs · Mathematics 2014-03-03 Rémi Carles , Hichem Hajaiej

The aim of this work is multifold. Firstly, it intends to present a complete, quantitative and self-contained description of the periodic traveling wave solutions and Whitham modulation equations for the Toda lattice, combining results from…

Exactly Solvable and Integrable Systems · Physics 2024-11-12 Gino Biondini , Christopher Chong , Panayotis Kevrekidis

We study one dimensional mixtures of two-component Bose-Einstein condensates in the limit where the intra-species and inter-species interaction constants are very close. Near the mixing-demixing transition the polarization and the density…

Quantum Gases · Physics 2018-04-20 T. Congy , A. M. Kamchatnov , N. Pavloff

The present paper is concerned with the existence of solitary wave solutions of Rosenau-type equations. By using two standard theories, Normal Form Theory and Concentration-Compactness Theory, some results of existence of solitary waves of…

Analysis of PDEs · Mathematics 2024-03-12 A. Durán , G. M. Muslu

In the framework of Gurevich and Pitaevskii approach [1] we construct modulated by Whitham [2] solution of nonlinear Shrodinger (NS) equation partially saturating the modulational instability. This solution describes new scenario of…

patt-sol · Physics 2008-02-03 Ramil' F. Bikbaev , Vadim R. Kudashev

The problem of wave breaking during its propagation in the Bose-Einstein condensate to a stationary medium is considered for the case when the initial profile at the breaking instant can be approximated by a power function of the form…

Pattern Formation and Solitons · Physics 2018-12-31 A. M. Kamchatnov

The magnetically induced Richtmyer-Meshkov instability in a two-component Bose-Einstein condensate is investigated. We construct and study analytical models describing the development of the instability at both the linear and nonlinear…

Quantum Gases · Physics 2015-05-19 A. Bezett , V. Bychkov , E. Lundh , D. Kobyakov , M. Marklund

The Gross-Pitaevskii equation for a Bose-Einstein condensate (BEC) with symmetric harmonic trap is given in (1). Periodic solutions of (1) play an important role in the understanding of the long term behavior of its solutions. In this note…

Analysis of PDEs · Mathematics 2016-03-08 Andres Contreras , Carlos García-Azpeitia

Generation of wave structures by a two-dimensional object (laser beam) moving in a two-dimensional two-component Bose-Einstein condensate with a velocity greater than both sound velocities of the mixture is studied by means of analytical…

Other Condensed Matter · Physics 2009-11-13 Yu. G. Gladush , A. M. Kamchatnov , Z. Shi , P. G. Kevrekidis , D. J. Frantzeskakis , B. A. Malomed

The creation and propagation of sound waves in two-component Bose-Einstein condensates (BEC) are investigated and a new method of wave generation in binary BEC mixtures is proposed. The method is based on a fast change of the inter-species…

Other Condensed Matter · Physics 2008-11-14 B. B. Baizakov , A. M. Kamchatnov , M. Salerno

In this work, we investigate the modulational instability of plane wave solutions within a modified Gross-Pitaevskii equation framework. The equation features cubic and quartic nonlinearity. It models the behaviour of quasi-one-dimensional…

Quantum Gases · Physics 2024-05-20 Sherzod R. Otajonov , Bakhram A. Umarov , Fatkhulla Kh. Abdullaev

In this paper, we investigate the existence and spectral stability of periodic traveling wave solutions for the regularized Camassa-Holm equation. To establish the existence of periodic waves, we employ tools from bifurcation theory to…

Analysis of PDEs · Mathematics 2026-03-03 Fabio Natali

The periodic standing wave method studies circular orbits of compact objects coupled to helically symmetric standing wave gravitational fields. From this solution an approximation is extracted for the strong field, slowly inspiralling…

General Relativity and Quantum Cosmology · Physics 2009-03-24 Napoleon Hernandez , Richard H. Price

Properties of localized states on array of BEC confined to a potential, representing superposition of linear and nonlinear optical lattices are investigated. For a shallow lattice case the coupled mode system has been derived. The…

Other Condensed Matter · Physics 2009-11-11 Fatkhulla Abdullaev , Abdulaziz Abdumalikov , Ravil Galimzyanov

We consider Bloch oscillations of Bose-Einstein condensates in presence of a time-modulated s-wave scattering length. Generically, interaction leads to dephasing and decay of the wave packet. Based on a cyclic-time argument, we…

The interaction between planetary waves and an arbitrary zonal flow is studied from a phase-space viewpoint. Using the Wigner distribution, a planetary wave Vlasov equation is derived that includes the contribution of the mean flow to the…

Fluid Dynamics · Physics 2010-10-27 Robin D. Wordsworth

The Bogoliubov equations are solved for a three-dimensional Bose-Einstein condensate containing a doubly quantized vortex, trapped in a harmonic potential. Complex frequencies, signifying dynamical instability, are found for certain ranges…

Other Condensed Matter · Physics 2009-11-11 Emil Lundh , Halvor M. Nilsen

Bose-Einstein condensates with an attractive 1/r interaction and with dipole-dipole interaction are investigated in the framework of the Gaussian variational ansatz introduced by S. Rau, J. Main, and G. Wunner [Phys. Rev. A, submitted]. We…

Quantum Gases · Physics 2010-08-17 Stefan Rau , Jörg Main , Holger Cartarius , Patrick Köberle , Günter Wunner

We study the stability and dynamics of vortices in two-species condensates using a two mode model. The recent experimental results obtained at JILA (M. R. Matthews, {\em et al.}, Phys. Rev. Lett. 83 (1999) 2498) and theoretical predictions…

Condensed Matter · Physics 2007-05-23 Victor M. Perez-Garcia , Juan J. Garcia-Ripoll

Breathers and rogue waves of special coupled nonlinear Schr\"odinger systems (the Manakov equations) are studied analytically. These systems model the orthogonal polarization modes in an optical fiber with randomly varying birefringence.…

Pattern Formation and Solitons · Physics 2014-10-29 Jin Hua Li , Hiu Ning Chan , Kin Seng Chiang , Kwok Wing Chow