Oblique resonant optical solitons with Kerr and parabolic law nonlinearities and fractional temporal evolution by generalized exp(−Φ(ξ))-expansion

Ferdous, F.; Hafez, M. G.; Biswas, Anjan; Ekici, Mehmet; Zhou, Qin; Alfiras, Mohanad; Moshokoa, Seithuti P.; Belić, Milivoj R.

doi:10.1016/j.ijleo.2018.10.016

Cited by 41 publications

(13 citation statements)

References 30 publications

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“…Figure 1 displays the nonlinear resonance wave phenomena by assuming the obtaining solutions Eq. (24) and Eq. (25) of the coupled NLSE having fractional time evolution for different values of obliqueness ( Ω ), fractional parameter ( ) and time (t) with the constant values of remaining parameter.…”

Section: Resultsmentioning

confidence: 99%

“…But, there are so many physical processes are still unknown to study the physical scenarios that challenged continue to determine the analytical solutions of fractional nonlinear evolution equations (FNLEEs). For this reason, scholars [22][23][24][25][26][27][28][29][30] are growing consideration to study the behavior of physical issues in science and engineering by evaluating the solutions of FNLEEs.…”

Section: Introductionmentioning

confidence: 99%

“…Conversely, references [31][32][33][34][35][36] have only constructed the analytical wave solutions of FNLEEs by overlooking obliqueness via the mathematical techniques. Very recently, a few authors [22][23][24] have only focused the influence of obliqueness on the analytical wave solutions of FNLEEs by considering the mathematical techniques, especially, the generalized exp(− φ(ξ))-expansion method and the modified Kudryashov method. They have reported that the obliqueness extensively modified the nature of wave dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Resonance nonlinear wave phenomena with obliqueness and fractional time evolution via the novel auxiliary ordinary differential equation method

2019

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In this article, the oblique resonance wave phenomena are investigated by considering nonlinear coupled evolution equations with fractional time evolution. In order to investigate such physical phenomena arising in many branches of physics, the time fractional coupled (2 + 1)-dimensional nonlinear Schrodinger and long-short wave resonance interaction evolution equations are considered. The analytical solutions of considered equations are achieved by implementing the proposed auxiliary ordinary differential equation method along with the properties of Khali's fractional derivatives. The obtained outcomes may be useful for better understanding the basic properties of internal oblique propagating wave dynamics in many branches of science and engineering.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Resonance nonlinear wave phenomena with obliqueness and fractional time evolution via the novel auxiliary ordinary differential equation method

2019

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“…Ρεςεντλψ, σομε σςηολαρς [45][46][47] αδοπτεδ τηε οβλιχυε ωα ε τρανσφορματιον το τηε φραςτιοναλ ΠΔΕς φορ δετερμινινγ οβλιχυε ωα ε σολυτιονς. Αφτερ υσινγ αν οβλιχυε ωα ε τρανσφορματιον σπεςιφιεδ βψ Εχ.…”

Section: αππλιςατιον οφ τηε γενεραλιζεδ κυδρψασηο μετηοδunclassified

Optical solutions to the Kundu-Mukherjee-Naskar equation: mathematical and graphical analysis with oblique wave propagation

Kumar

Paul

Biswas

et al. 2020

Preprint

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This paper retrieves some new optical solutions to the Kundu-Mukherjee-Naskar (KMN) equation in the context of nonlinear optical fiber communication systems. In this regard, the generalized Kudryashov and new auxiliary equation methods are applied to the KMN equation and consequently, dark, bright, periodic U-shaped and singular soliton solutions are explored. The discrepancies between the present obtained solutions and the previously obtained solutions by using different methods are discussed. The time fractional derivative and an oblique wave transformation in coordination with the methods of interest are considered for acquiring new optical wave solutions of the KMN equation in the sense of conformable derivative and wave obliqueness, respectively. The effects of obliqueness and fractionality on the attained solutions are demonstrated graphically along with its physical descriptions. It is found that the optical wave phenomena are changed with the increase of obliqueness as well as fractionality. All the obtained optical solutions are found to be new in the sense of conformable derivative, wave obliqueness, and the applied methods. Finally, it is found that the utilized methods and the relevant transformation are powerful over the other methods and it can be applicable for further studies to explain the pragmatic phenomena in optical fiber communication systems.

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“…Thus, many new methods have been proposed, such as the tanh-sech method [14][15][16], Jacobi elliptic function method [17][18][19], exp-function method [20,21], sine-cosine method [22][23][24], homogeneous balance method [25,26], F-expansion method [27,28], extended tanh-method [29,30], (G /G)− expansion method [31,32]. Indeed, there are recent development in analytical and numerical methods for finding solutions for NPDEs, see [33][34][35][36][37][38][39][40][41][42][43][44] and references therein.…”

Section: Introductionmentioning

confidence: 99%

The new exact solutions for the deterministic and stochastic (2+1)-dimensional equations in natural sciences

Abdelrahman

Sohaly

Alharbi

2019

Journal of Taibah University for Science

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This paper poses the Riccati-Bernoulli sub-ODE method in order to find the exact (random) travelling wave solutions for the (2+1)-dimensional cubic nonlinear Klein-Gordon (cKG) equation and the (2+1)-dimensional nonlinear Zakharov-Kuznetsov modified equal width (ZK-MEW) equation. The obtained travelling wave solutions are expressed by the hyperbolic, trigonometric and rational functions. Indeed, these solutions reflect some interesting physical interpretation for nonlinear phenomena. We discuss our method in deterministic case and in a random case. Additionally, we can show and discuss this method under some random distributions. Finally, some three-dimensional graphics of some solutions have been illustrated.

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Oblique resonant optical solitons with Kerr and parabolic law nonlinearities and fractional temporal evolution by generalized exp(−Φ(ξ))-expansion

Cited by 41 publications

References 30 publications

Resonance nonlinear wave phenomena with obliqueness and fractional time evolution via the novel auxiliary ordinary differential equation method

Resonance nonlinear wave phenomena with obliqueness and fractional time evolution via the novel auxiliary ordinary differential equation method

Optical solutions to the Kundu-Mukherjee-Naskar equation: mathematical and graphical analysis with oblique wave propagation

The new exact solutions for the deterministic and stochastic (2+1)-dimensional equations in natural sciences

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