Some new families of solitary wave solutions of the generalized Schamel equation and their applications in plasma physics

Cheemaa, Nadia; Seadawy, Aly R.; Chen, Sheng

doi:10.1140/epjp/i2019-12467-7

Cited by 95 publications

(22 citation statements)

References 46 publications

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“…The study of integrable nonlinear systems has become a hot topic in wave propagations and mathematical physics. Integrable systems approximately describe the evolution of various waves in many physical settings, including shallowwater waves with weakly nonlinear restoring forces, pulse propagation in optical fibers and wave guides, long internal waves in a density-stratified ocean, and ion acoustic waves in plasma [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. In the higher-dimensional extensions of integrable nonlinear wave equation, the (2+1)-dimensional KdV equation or the asymmetrical Nizhnik-Novikov-Veselov (ANNV) equation [17] u t + u xxx + 3 u∂ −1 y u x…”

Section: Introductionmentioning

confidence: 99%

“…Although these results can also be derived by Darboux transformation [47][48][49][50], modified extended mapping method [1], and direct algebraic method [2], the bilinear method is still a powerful tool for solving integrable systems. It is worth mentioning that Seadawy et al obtained some new exact solutions of many integrable systems by using various methods, such as extend simple equation method and the exp ðϕðξÞÞ expansion method [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. For the ANNV equation (1), the lump solutions, mixed lump-stripe solutions, and periodic lump solutions were presented in [19].…”

Section: Introductionmentioning

confidence: 99%

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Mixed Rational Lump-Solitary Wave Solutions to an Extended (2+1)-Dimensional KdV Equation

Yao

Xie

Hui

2021

Advances in Mathematical Physics

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Based on the bilinear method, rational lump and mixed lump-solitary wave solutions to an extended (2+1)-dimensional KdV equation are constructed through the different assumptions of the auxiliary function in the trilinear form. It is found that the rational lump decays algebraically in all directions in the space plane and its amplitude possesses one maximum and two minima. One kind of the mixed solution describes the interaction between one lump and one line solitary wave, which exhibits fission and fusion phenomena under the different parameters. The other kind of the mixed solution shows one lump interacting with two paralleled line solitary waves, in which the evolution of the lump gives rise to a two-dimensional rogue wave. This shows that these three interesting phenomena exist in the corresponding physical model.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mixed Rational Lump-Solitary Wave Solutions to an Extended (2+1)-Dimensional KdV Equation

Yao

Xie

Hui

2021

Advances in Mathematical Physics

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“…Extracting exact solutions of nonlinear partial differential equations is also important to check the stability of numerical solutions as well as to develop a wide range of new mathematical solvers to simplify the calculation. In recent time, an abundance of new more powerful and effective methods have been developed with the help of different computer softwares like Mathematica, Maple and Matlab, such as the Kudryashov method, the truncated expansion method, the Boacklund transform method , the inverse scattering method, the extended Fan sub-equation method, the homogeneous balance method, the Jacobi elliptic function method, the tanh-function method, the BVI INIT Method and many more in several theoretical works about solitons and their applications [21], [22], [23], [24], [25], [26]. Nowadays, During studying the ultrashort pulses, the higher-order nonlinear effects and high-order dispersion cannot be neglected.…”

Section: Introductionmentioning

confidence: 99%

Stability of Soliton Solutions For A PT- Symmetric NLDC Considering High-Order Dispersion and Nonlinear Effects Simultaneously

Safaei

Hatami

Zarandi

2021

Preprint

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In this paper, we analytically solve the coupled equations of a PT -Symmetric NLDC by considering high-order dispersion and nonlinear effects (Raman Scattering and self-steeping) simultaneously in normal dispersion regime. To the best of knowledge no works has been done in previous studies to decoupled these equations and obtain an exact analytical solution. The new exact bright solitary solutions are derived. In addition, to study the stability and instability of these propagated solitons in a PT -Symmetric NLDC, perturbation theory is used. Numerical methods are applied to find perturbed eigenvalues and eigenfunctions. The Stability of obtained four perturbed eigenvalues and perturbed eigenfunctions for a PT -Symmetric NLDC equations regard to high-order effects are examined. Using these results and simulating the propagation of perturbed temporal bright solitons through PT -Symmetric NLDC show that perturbed solitons are mostly stable. This means that high-order dispersion and nonlinear effects canceled each other and do not affected the propagated solitons. Furthermore, the evolution of perturbed solitons energies match well the previous results and con rmed the stability of these solitons in a PT -Symmetric NLDC. As seen the energies of pulses in bar and cross behave in two manner 1) the exchange of energy is happened in some periods, but the shape of each pulse in bar and cross is preserved. Therefore, the solitons under this eigenfunction perturbation are mostly stable. 2) the evolution of energy in the bar and cross, demonstrate that there is no changes in their energies and they remain constant. It is straightforward to show that in spite of considering high-order effects, the perturbed soliton conserve the shape and it remain stable. The deliverables of this article not only demonstrate a novel approach to ultra-fast pulses, solitons and optical couplers, but more fundamentally, they could give insight for improving the new medical equipments technologies, enabling innovations in nonlinear optics and their usage in designing new communication systems and Photonic devices.

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“…These solutions of NLPDEs provide better evidence about its physical structures. Due to this, different powerful and efficient algorithms 6‐21 were established to extract the exact solutions for nonlinear physical models 22‐28 …”

Section: Introductionmentioning

confidence: 99%

Dispersive of propagation wave solutions to unidirectional shallow water wave Dullin–Gottwald–Holm system and modulation instability analysis

Bilal

Seadawy

Younis

et al. 2020

Math Methods in App Sciences

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110

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This article possesses modulation instability (MI) analysis and new exact wave solutions to unidirectional Dullin–Gottwald–Holm (DGH) system that describes the prorogation of waves in shallow water. The exact wave solutions in single and combined form like shock, singular, and shock‐singular are extracted by means of an innovative integration norm, namely, ()G′false/G2‐expansion scheme. The periodic and plane wave solutions are also emerged. The constraint conditions which ensure the existence of solutions are discussed as well. Moreover, the choice of suitable parameters gives the three‐dimensional and two‐dimensional sketches, and furthermore, their contour plots are also drawn.

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Some new families of solitary wave solutions of the generalized Schamel equation and their applications in plasma physics

Cited by 95 publications

References 46 publications

Mixed Rational Lump-Solitary Wave Solutions to an Extended (2+1)-Dimensional KdV Equation

Mixed Rational Lump-Solitary Wave Solutions to an Extended (2+1)-Dimensional KdV Equation

Stability of Soliton Solutions For A PT- Symmetric NLDC Considering High-Order Dispersion and Nonlinear Effects Simultaneously

Dispersive of propagation wave solutions to unidirectional shallow water wave Dullin–Gottwald–Holm system and modulation instability analysis

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