Modified Kudryashov method and its application to the fractional version of the variety of Boussinesq-like equations in shallow water

Kumar, Dipankar; Darvishi, M. T.; Joardar, Atish Kumar

doi:10.1007/s11082-018-1399-y

Cited by 38 publications

(19 citation statements)

References 40 publications

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“…We present a succinct about the modified Kudryashov method [11,12] producing new exact solutions for a given nonlinear partial differential equation.…”

Section: Algorithm Of Modified Kudryashov Methodsmentioning

confidence: 99%

“…Because of the growing progress of computer and computation technologies and artificial intelligence based symbolic computation like as Maple, Mathematica and MATLAB, several analytical approaches have attempt and aptly applied to look for more general and newer exact solutions of nonlinear integer and fractional order partial differential equations (NPDEs) such as the Lie symmetry analysis [1], extended trial equation method [2,3], functional variable method [4], Kudryashov's method [4], Jacobian elliptic equations expansion method [5,6], exp (−φ(ξ))-expansion method [7], semi-inverse variational principle [8], ansatz method [9], (G /G)-expansion method [10], modified Kudryashov's method [11,12], sine-Gordon expansion method [13,14], extended sinh-Gordon expansion method [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

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Optical Soliton in Nonlocal Nonlinear Medium with Cubic-Quintic Nonlinearities and Spatio-Temporal Dispersion

et al. 2018

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In this article, we have constructed some new soliton solutions of the nonlocal nonlinear medium equation via three reliable approaches. The executed approaches are modified Kudryashov method, sinh-Gordon equation expansion method and extended sinh-Gordon equation expansion method. In this case, there are three types of competing nonlinearities that are taken into account in our model. They are nonlocal nonlinearity, cubic nonlinearity, and quintic nonlinearity. By means of the aforementioned methods, dark, bright, combined dark-bright, singular, combined singular, periodic, and other soliton solutions are obtained from the nonlocal nonlinear medium equation, and their respective existence conditions.

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“…We present a succinct about the modified Kudryashov method [11,12] producing new exact solutions for a given nonlinear partial differential equation.…”

Section: Algorithm Of Modified Kudryashov Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optical Soliton in Nonlocal Nonlinear Medium with Cubic-Quintic Nonlinearities and Spatio-Temporal Dispersion

et al. 2018

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“…Σιξτψ οπτιςαλ ωα ε σολυτιονς αρε εξπλορεδ, ωηιςη αρε νεω ιν τηε σενσε οφ ςονφορμαβλε φραςτιοναλ δερι ατι ε. Σομε αππλιςατιονς οφ ςονφορμαβλε δερι ατι ε το ΝΠΔΕς αρε α αιλαβλε ιν ρεφς. [42][43][44]. Φορ τηε σακε οφ στραιγητφορωαρδνεσς, ωε ηα ε ινςλυδεδ φουρ σολυτιονς οβταινεδ ια τηε γΚΜ ανδ τηε ΝΑΕΜ ιν τηε σενσε οφ ςονφορμαβλε φραςτιοναλ δερι ατι ε. Οπτιςαλ ωα ε σολυτιονς οφ τηε τιμε φραςτιοναλ ΚΜΝ εχυατιον βψ τηε γΚΜ αρε γι εν βελοω:…”

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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“…This fact motivated researchers to take an interest in the study of fractional in time and/or space evolution equations. In particular, the study of analytic and numerical solutions of fractional shallow-water equations was investigated by many authors (see e.g., [5,[9][10][11][12]). For the study of existence and non-existence of global solutions for fractional in time and/or space evolution equations, we refer to [13][14][15] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Absence of Global Solutions for a Fractional in Time and Space Shallow-Water System

2019

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Modified Kudryashov method and its application to the fractional version of the variety of Boussinesq-like equations in shallow water

Cited by 38 publications

References 40 publications

Optical Soliton in Nonlocal Nonlinear Medium with Cubic-Quintic Nonlinearities and Spatio-Temporal Dispersion

Optical Soliton in Nonlocal Nonlinear Medium with Cubic-Quintic Nonlinearities and Spatio-Temporal Dispersion

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

Absence of Global Solutions for a Fractional in Time and Space Shallow-Water System

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