Multihump soliton-like structures in interactions of lasers and Bose-Einstein condensates

Cattani, Federica; Kim, A. V.; Hansson, Tobias; Anderson, D.; Lisak, M.

doi:10.1209/0295-5075/94/53003

Cited by 4 publications

(2 citation statements)

References 18 publications

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“…Such type of multipeaked stationary solutions exist in laser-BEC interactions and it has been shown that they can also explain the formation of bound state. Also, these triple-peak nonlinear wave can be associated with a series of asymmetric optical multipeak solitons on a continuous wave background [22].…”

Section: Case (I): X 1 + Ax 2 (Travelling Wave Solutions)mentioning

confidence: 99%

Lie symmetry analysis and group invariant solutions of the nonlinear Helmholtz equation

Sakkaravarthi

Johnpillai²,

Devi

et al. 2018

Applied Mathematics and Computation

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We consider the nonlinear Helmholtz (NLH) equation describing the beam propagation in a planar waveguide with Kerr-like nonlinearity under non-paraxial approximation. By applying the Lie symmetry analysis, we determine the Lie point symmetries and the corresponding symmetry reductions in the form of ordinary differential equations (ODEs) with the help of the optimal systems of one-dimensional subalgebras. Our investigation reveals an important fact that in spite of the original NLH equation being non-integrable, its symmetry reductions are of Painlevé integrable. We study the resulting sets of nonlinear ODEs analytically either by constructing the integrals of motion using the modified Prelle-Singer method or by obtaining explicit travelling wave-like solutions including solitary and symbiotic solitary wave solutions. Also, we carry out a detailed numerical analysis of the reduced equations and obtain multi-peak nonlinear wave trains. As a special case of the NLH equation, we also make a comparison between the symmetries of the present NLH system and that of the standard nonlinear Schrödinger equation for which symmetries are long available in the literature.

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Section: Case (I): X 1 + Ax 2 (Travelling Wave Solutions)mentioning

confidence: 99%

Lie symmetry analysis and group invariant solutions of the nonlinear Helmholtz equation

Sakkaravarthi

Johnpillai²,

Devi

et al. 2018

Applied Mathematics and Computation

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“…For nonintegrable multi-component nonlinear models formation of stable multihump solitary waves, a novel physical mechanism has been presented in [5]. These multi-hump optical solitons observed numerically in the models describing laser radiation copropagating with a Bose-Einstein condensate and used to shed light on the phenomenon of jet emission from a condensate interacting with a laser [6].…”

Section: Introductionmentioning

confidence: 99%

New multi-hump exact solitons of a coupled Korteweg-de-Vries system with conformable derivative describing shallow water waves via RCAM

Das¹

2020

Phys. Scr.

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In this article, a modification of the rapidly convergent approximation method is proposed to solve a coupled Korteweg–de Vries equations with conformable derivative that govern shallow-water waves. Based on the Leibniz and chain rule of conformable derivative, these equations reduced into ODEs with integer-order using traveling wave transformation. Adopting the modified scheme a new novel exact solution of the reduced coupled ordinary differential equations is obtained in terms of exponential functions. Finally, by putting them back into traveling wave transformation the solutions of the considered partial differential equations with conformable derivative are derived. To ensure the boundedness of the derived solutions few theorems have been proposed and proved. The derived results of the theorems are utilized to plot the solutions. Graphics exhibit that solutions have variant multi-hump soliton peculiarities and their tails decay to zero exponentially in a monotonic manner. These results not only show the efficiency of the modified scheme but also establish that the solution is enriched with new multi-hump features.

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The interaction of three long shallow-water waves with different dispersion relations modeled by generalized Hirota–Satsuma KdV systems with some variable coefficients

Das

2023

Nonlinear Dyn

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Multihump soliton-like structures in interactions of lasers and Bose-Einstein condensates

Cited by 4 publications

References 18 publications

Lie symmetry analysis and group invariant solutions of the nonlinear Helmholtz equation

Lie symmetry analysis and group invariant solutions of the nonlinear Helmholtz equation

New multi-hump exact solitons of a coupled Korteweg-de-Vries system with conformable derivative describing shallow water waves via RCAM

The interaction of three long shallow-water waves with different dispersion relations modeled by generalized Hirota–Satsuma KdV systems with some variable coefficients

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