On the physical nonlinear (n＋1)-dimensional Schrödinger equation applications

Abdelwahed, H. G.; El-Shewy, Ε. K.; Abdelrahman, Mahmoud A. E.; Alsarhana, A. F.

doi:10.1016/j.rinp.2020.103798

Cited by 37 publications

(9 citation statements)

References 39 publications

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“…The study of solitary waves is also related to the study of plasma physics, which contains charged particles in large numbers [ 33 ]. For example, the KdV equation reflects the change of charge from neutrality.…”

Section: Applications Of Solitonsmentioning

confidence: 99%

Soliton: A dispersion-less solution with existence and its types

Arora

Rani

Emadifar

2022

Heliyon

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Section: Applications Of Solitonsmentioning

confidence: 99%

Soliton: A dispersion-less solution with existence and its types

Arora

Rani

Emadifar

2022

Heliyon

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“…see for example [28][29][30][31][32][33][34][35][36]. As a result of the importance of the deterministic Eq.…”

Section: Introductionmentioning

confidence: 99%

The new stochastic solutions to the perturbed NLSE

Abdelwahed,

abdelrahman

2024

Preprint

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This article extracts exact solutions for the perturbed nonlinear Schrödinger’s equation (PNLSE) with Kerr law nonlinearity forced by multiplicative noise in It^o sense by utilizing the unified solver method. The presented solutions involve three types: rational function, trigonometric function and hyperbolic function solutions. These stochastic solutions may be applicable for investigation various complex phenomena in applied science and new physics. We exhibit the influence of multiplicative noise on the solution of the PNLSE forced by multiplicative noise in It^o sense. The study and acquired solutions clarify that the unified solver technique is sturdy and efficient. Finally, some 3D proles to some of the gained solutions are also illustrated.

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“… 20 – 23 . The physical exact nonlinear solutions of the (n+1)-dimensional Schrödinger are obtained using RB sub-ODE and He’s semi-inverse techniques, and several types of solutions, bright optical and dark solitons are derived in 24 . Some extract new solutions of space-time stochastic fractional nonlinear Schrödinger equation with spatiotemporal dispersion are presented, and some new stochastic solutions with physical parameters are constructed via exponential distribution in 25 .…”

Section: Introductionmentioning

confidence: 99%

Some anomalous exact solutions for the four-component coupled nonlinear Schrödinger equations on complex wave backgrounds

Wang

2022

Sci Rep

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The coupled nonlinear Schrödinger (CNLS) equations are the important models for the study of the multicomponent Bose-Einstein condensates (BECs). In this paper, we study the four-components CNLS equations via Darboux transformation and obtain the N-soliton solutions with zero seed and non-zero seed solutions($$q_i=0$$ q i = 0 or $$q_i=e^{-2it})$$ q i = e - 2 i t ) . The 1-soliton solution and 2-soliton solution are calculated on complex wave backgrounds, the dark-bright-bright-bright soliton solutions and dark-dark-bright-bright soliton solutions are constructed. We can obtain a new class of dark-bright-bright-bright soliton solutions, which admit one-valley dark soliton in component $$q_1$$ q 1 and triple-hump bright solitons in the other three components. The collision properties between dark-dark-bright-bright solitons are considered, and the vector solitons are expected to be much more abundant than those of previously reported vector soliton collisions.

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On the physical nonlinear (n＋1)-dimensional Schrödinger equation applications

Cited by 37 publications

References 39 publications

Soliton: A dispersion-less solution with existence and its types

Soliton: A dispersion-less solution with existence and its types

The new stochastic solutions to the perturbed NLSE

Some anomalous exact solutions for the four-component coupled nonlinear Schrödinger equations on complex wave backgrounds

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