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

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Using Gauge transformation method, we generate rogue waves for the two component Bose Einstein Condensates (BECs) governed by the symmetric coupled Gross-Pitaevskii (GP) equations and study their dynamics. We also suggest a mechanism to…

Other Condensed Matter · Physics 2013-09-25 P. S. Vinayagam , R. Radha , K. Porsezian

The Whitham modulation equations for the parameters of a periodic solution are derived using the generalized Lagrangian approach for the case of damped Benjamin-Ono equation. The structure of the dispersive shock in internal wave in deep…

Pattern Formation and Solitons · Physics 2007-06-07 Y. Matsuno , V. S. Shchesnovich , A. M. Kamchatnov , R. A. Kraenkel

In this work, we explore the rogue wave patterns in the coupled Fokas-Lenells equation by using the Darboux transformation. We demonstrate that when one of the internal parameters is large enough, the general high-order rogue wave solutions…

Exactly Solvable and Integrable Systems · Physics 2023-07-06 Liming Ling , Huajie Su

Numerical simulations of the recently derived fully nonlinear equations of motion for weakly three-dimensional water waves [V.P. Ruban, Phys. Rev. E {\bf 71}, 055303(R) (2005)] with quasi-random initial conditions are reported, which show…

Fluid Dynamics · Physics 2009-11-11 Victor P. Ruban

Experimental results describing random, uni-directional, long crested, water waves over non-uniform bathymetry confirm the formation of stable coherent wave packages traveling with almost uniform group velocity. The waves are generated with…

Pattern Formation and Solitons · Physics 2020-08-12 A. Wang , A. Ludu , Z. Zong , L. Zou , Y. Pei

Considered in this paper is a bi-directional model for the propagation of interfacial capillary-gravity waves in a two-layer system of fluids with rigid lid condition for the upper layer and lower layer with a much larger or infinite depth.…

Analysis of PDEs · Mathematics 2020-04-28 A. Durán

We investigate the two-dimensional modified Gross-Pitaevskii equation, accounting for the effects of atom gain/loss and a time-independent isotropic confining potential, utilizing the Hirota's bilinear method. Through an appropriate…

Quantum Gases · Physics 2025-04-29 C. E. Nkenfack , O. T. Lekeufack , S. Sabari , R. Yamapi , T. C. Kofane

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

Using the generalised nonlinear Schr\"odinger equation, we investigate how the effect of third-order dispersion, self-steepening, and Raman-induced-self-frequency shift have an impact on the higher-order rogue waves. We observe that…

Pattern Formation and Solitons · Physics 2022-10-04 Amdad Chowdury , Wonkeun Chang , Marco Battiato

In this paper, using the Darboux transformation, we demonstrate the generation of first order breather and higher-order rogue waves from a generalized nonlinear Schr\"odinger equation with several higher-order nonlinear effects representing…

Exactly Solvable and Integrable Systems · Physics 2013-06-06 L. H. Wang , K. Porsezian , J. S. He

In this work, we focus on the construction of Nth-rouge wave solutions for the Hirota equation by utilizing the bilinear method. The formula can be represented in terms of determinants. In addition, some interesting dynamic patterns of…

Exactly Solvable and Integrable Systems · Physics 2014-09-24 Gui Mu , Zhenyun Qin

We consider a two-level atomic system, interacting with an electromagnetic field controlled in amplitude and frequency by a high intensity laser. We show that the amplitude of the induced electric field, admits an envelope profile…

Pattern Formation and Solitons · Physics 2016-08-24 Jingsong He , Shuwei Xu , K. Porsezian , Yi Cheng , P. Tchofo Dinda

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

A specific, genuinely three-dimensional mechanism of rogue wave formation, in a late stage of the modulational instability of a perturbed Stokes deep-water wave, is recognized through numerical experiments. The simulations are based on…

Fluid Dynamics · Physics 2007-08-01 V. P. Ruban

The rogue waves in a resonant erbium-doped fibre system governed by a coupled system of the nonlinear Schr\"odinger equation and the Maxwell-Bloch equation (NLS-MB equations) are given explicitly by a Taylor series expansion about the…

Exactly Solvable and Integrable Systems · Physics 2015-06-11 Jingsong He , Shuwei Xu , K. Porseizan

In different nonlinear mediums, the wave trains carry energy and expose many amazing features. To describe a nonlinear phenomenon, a soliton is one that preserves its shape and amplitude even after the collision. Breather is one kind of…

This study investigates the numerical evolution of an initially internal random wave field characterized by a Gaussian spectrum shape using the Benjamin-Ono (BO) equation. The research focuses on analyzing various properties associated with…

Fluid Dynamics · Physics 2023-07-18 Marcelo V. Flamarion , Efim Pelinovsky

In this paper, we give the first rigorous justification of the Benjamin-Ono equation as an internal water wave model on the physical time scale. Let $\varepsilon$ be the small parameter measuring the weak nonlinearity of the waves, $\mu$ be…

Analysis of PDEs · Mathematics 2024-10-31 Martin Oen Paulsen

In this paper, a generalized long-wave short-wave resonance interaction system, which describes the nonlinear interaction between a short-wave and a long-wave in fluid dynamics, plasma physics and nonlinear optics, is considered. Using the…

Pattern Formation and Solitons · Physics 2022-06-22 M. Kirane , S. Stalin , M. Lakshmanan

Under investigation is a new (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. The main results are listed as follows: (i) lump solutions; (ii) Interaction solutions between lump wave and solitary waves; (iii) Interaction solutions…

Pattern Formation and Solitons · Physics 2020-10-27 Jian-Guo Liu , Abdul-Majid Wazwaz