Dark and bright soliton solutions and computational modeling of nonlinear regularized long wave model

Kumar, Sanjay; Jiwari, Ram; Mittal, R. C.; Awrejcewicz, Jan

doi:10.1007/s11071-021-06291-9

Cited by 36 publications

(7 citation statements)

References 54 publications

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“…Indeed, we concentrate our attention on the nonlinear Schrödinger equation that models the dynamic of waves in such materials. The arising solitons and other analytical solutions to different forms of Schrödinger models have been widely studied by the authors [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The few-cycle pulse propagation in metamaterials specially is one of nonlinear Schrödinger applications and its solutions are helpful to understands more deeply the concerned materials.…”

Section: -Introductionmentioning

confidence: 99%

New lump solutions to the nonlinear Schrödinger equation under the few-cycle pulse propagation property

Zahran

Bekir²

2023

Preprint

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Throughout this work, we will derive new various types of lump solutions to the nonlinear Schrödinger equation that describing few-cycle pulse propagation in metamaterials. The propagation of waves through optical fibre is one of recent phenomenon that plays fundamental rule in all telecommunication processes as well as medicine devices industries, ocean engineering devices technologies. The lump solutions of this model will be firstly constructed in this article via three various techniques which are the (G’/G)-expansion method, the extended simple equation method (ESEM) and the Paul-Painleve approach method (PPAM). These three techniques have been regularly implemented in parallel paths to show the agreements between the output results. When the comparison between our achieved results with each other’s as well as by that achieved previously has been implemented, it shows the novelty of these results.

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Section: -Introductionmentioning

confidence: 99%

New lump solutions to the nonlinear Schrödinger equation under the few-cycle pulse propagation property

Zahran

Bekir²

2023

Preprint

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“…In 1990, Kansa first applied the collocation method and RBFs method with application to computational fluid dynamics [19,20]. After that, there are lots of research works on the applications of the RBFs collocation methods (see [11,[21][22][23][24][25][26][27][28][29][30][31] and their references). The collocation method with RBFs is a real meshless method for solving PDEs, and it is independent of the spatial dimensions [17,32].…”

Section: Introductionmentioning

confidence: 99%

A novel local Hermite radial basis function‐based differential quadrature method for solving two‐dimensional variable‐order time fractional advection–diffusion equation with Neumann boundary conditions

Liu

2023

Numerical Methods Partial

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A novel Hermite radial basis function-based differential quadrature (H-RBF-DQ) method is presented in this paper based on 2D variable order time fractional advection-diffusion equations with Neumann boundary conditions. The proposed method is designed to treat accurately for derivative boundary conditions, which considerably improve the approximation results and extend the range of applicability for the method of RBF-DQ. The advantage of the present method is that the Hermite interpolation coefficients are only dependent of the point distribution yielding a substantially better imposition of boundary conditions, even for time evolution. The proposed algorithm is thoroughly validated and is demonstrated to handle the fractional calculus problems with both Dirichlet and Neumann boundaries very well.

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“…ere are several technical methods for solving and investigating several kind of nonlinear partial differential equations, e.g. [44][45][46][47][48][49][50][51][52][53][54][55][56][57][58].…”

Section: Introductionmentioning

confidence: 99%

Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model

Elmandouh

Elbrolosy

2022

Journal of Mathematics

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The Ivancevic option pricing model comes as an alternative to the Black-Scholes model and depicts a controlled Brownian motion associated with the nonlinear Schrodinger equation. The applicability and practicality of this model have been studied by many researchers, but the analytical approach has been virtually absent from the literature. This study intends to examine some dynamic features of this model. By using the well-known ARS algorithm, it is demonstrated that this model is not integrable in the Painlevé sense. He’s variational method is utilized to create new abundant solutions, which contain the bright soliton, bright-like soliton, kinky-bright soliton, and periodic solution. The bifurcation theory is applied to investigate the phase portrait and to study some dynamical behavior of this model. Furthermore, we introduce a classification of the wave solutions into periodic, super periodic, kink, and solitary solutions according to the type of the phase plane orbits. Some 3D-graphical representations of some of the obtained solutions are displayed. The influence of the model’s parameters on the obtained wave solutions is discussed and clarified graphically.

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Dark and bright soliton solutions and computational modeling of nonlinear regularized long wave model

Cited by 36 publications

References 54 publications

New lump solutions to the nonlinear Schrödinger equation under the few-cycle pulse propagation property

New lump solutions to the nonlinear Schrödinger equation under the few-cycle pulse propagation property

A novel local Hermite radial basis function‐based differential quadrature method for solving two‐dimensional variable‐order time fractional advection–diffusion equation with Neumann boundary conditions

Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model

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