Highly dispersive optical solitons with quadratic–cubic law of refractive index by the variational iteration method

González-Gaxiola, O.; Biswas, Anjan; Ekici, Mehmet; Khan, Salam

doi:10.1007/s12596-020-00671-x

Cited by 39 publications

(9 citation statements)

References 33 publications

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“…These approaches should include establishing conservation laws, addressing the aspect of optical-soliton cooling, implementing a variational principle to recover dynamics of soliton parameters, applying a Laplace-Adomian decomposition scheme for studying the model numerically, applying a symmetry method, and some others techniques (see Refs. [16][17][18][19][20][21][22][23][24][25]).…”

Section: Discussionmentioning

confidence: 99%

Cubic�quartic optical solitons having quadratic�cubic nonlinearity by sine�Gordon equation approach

et al. 2021

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Section: Discussionmentioning

confidence: 99%

Cubic�quartic optical solitons having quadratic�cubic nonlinearity by sine�Gordon equation approach

et al. 2021

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“…where 𝜙(𝜍, 𝜏) is IShT of the first and last term of (28) considering together. Now, applying the ADM [42] to Equation (28) gives…”

Section: Case -(I)mentioning

confidence: 99%

“…Numerous successful analytical approaches have been formulated to solve fractional differential equations, including the variational iteration method (VIM) [28], Adomian decomposition method (ADM) [29], homotopy perturbation method (HPM) [30], and residual power series method (RPSM) [31]. In the last two decades, several integral transforms [32][33][34][35] in the Laplace transform class have been constructed.…”

mentioning

confidence: 99%

Solution of fractional Sawada–Kotera–Ito equation using Caputo and Atangana–Baleanu derivatives

Khirsariya

Rao

2023

Math Methods in App Sciences

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In the present work, the fractional‐order Sawada–Kotera–Ito problem is solved by considering nonlocal Caputo and nonsingular Atangana–Baleanu (ABC) derivatives. The methodology used is an application of the Shehu transform and the Adomian decomposition method. The obtained solution is more accurate when using the ABC type derivative as compared to the Caputo sense, when using the proposed ADShTM method (Adomian decomposition Shehu transform method). The results so obtained by the ADShTM using Caputo and ABC operators are compared, establishing the superiority of the proposed method. The numerical results demonstrate that the application of the ABC derivative is not only relatively more effective and reliable but also straightforward to achieve high precision solution.

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“…Using linearization, successive, or perturbation methods, only approximate solutions can be obtained. Iterative Laplace transform method [10], Adomian decomposition method [11], Homotopy analysis method [12], operational matrix method [13], fractional differential transform method [14], Fourier transform technique [15], operational calculus method [16], Variational iteration method [17], Sumudu transform method [18], multistep generalised differential transform method [19], iterative reproducing kernel method [20], Homotopy perturbation method [21], and Numerical multistep method [22].…”

Section: Introductionmentioning

confidence: 99%

The Fractional Investigation of Some Nonlinear Partial Differential Equations by Using an Efficient Procedure

Tchier¹,

Khan²,

Khan³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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The nonlinearity in many problems occurs because of the complexity of the given physical phenomena. The present paper investigates the non-linear fractional partial differential equations' solutions using the Caputo operator with Laplace residual power series method. It is found that the present technique has a direct and simple implementation to solve the targeted problems. The comparison of the obtained solutions has been done with actual solutions to the problems. The fractional-order solutions are presented and considered to be the focal point of this research article. The results of the proposed technique are highly accurate and provide useful information about the actual dynamics of each problem. Because of the simple implementation, the present technique can be extended to solve other important fractional order problems.

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Highly dispersive optical solitons with quadratic–cubic law of refractive index by the variational iteration method

Cited by 39 publications

References 33 publications

Cubic�quartic optical solitons having quadratic�cubic nonlinearity by sine�Gordon equation approach

Cubic�quartic optical solitons having quadratic�cubic nonlinearity by sine�Gordon equation approach

Solution of fractional Sawada–Kotera–Ito equation using Caputo and Atangana–Baleanu derivatives

The Fractional Investigation of Some Nonlinear Partial Differential Equations by Using an Efficient Procedure

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