Exact optical solitons to the perturbed nonlinear Schrödinger equation with dual-power law of nonlinearity

Nestor, Savaïssou; Gambo, B.; Rezazadeh, Hadi; Bekir, Ahmet; Doka, Serge Y.

doi:10.1007/s11082-020-02412-7

Cited by 116 publications

(23 citation statements)

References 37 publications

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“…us, ψ(x, t) satisfies equation (1). Applying the third prolongation to (1), we have the accompanying deciding condition, which is given as…”

Section: Lie Symmetry and Reduction Of Fbbm Equationmentioning

confidence: 99%

“…Substituting 7and (8) into (16) and equaling coefficients in derivatives for x and power of u to zero, the system of equations is obtained: α 1 xt − η tψ � 0.…”

Section: Lie Symmetry and Reduction Of Fbbm Equationmentioning

confidence: 99%

“…where c 1 and c 2 are constants. By the previous infinitesimal, equation (1) has two vector fields in the form…”

Section: Lie Symmetry and Reduction Of Fbbm Equationmentioning

confidence: 99%

“…Partial differential equations running into the thinking of most of the researchers as it represented the importance in several topics of scientific fields as mechanics, optical fibers, medical sciences (as breast cancer), biological science, turbulent bursts, and oceans waves [1][2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…In Section 2, Lie's group method for FPDEs is exposed. In Section 3, we apply the Lie group reduction method to obtain Lie point symmetry for the time FBBM equation (1). At the end of Section 4, we use these similarity variables to get the reduced equation.…”

Section: Introductionmentioning

confidence: 99%

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Analytical Solutions for Nonlinear Dispersive Physical Model

Ali

Sadat

2020

Complexity

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Nonlinear evolution equations widely describe phenomena in various fields of science, such as plasma, nuclear physics, chemical reactions, optics, shallow water waves, fluid dynamics, signal processing, and image processing. In the present work, the derivation and analysis of Lie symmetries are presented for the time-fractional Benjamin–Bona–Mahony equation (FBBM) with the Riemann–Liouville derivatives. The time FBBM equation is reduced to a nonlinear fractional ordinary differential equation (NLFODE) using its Lie symmetries. These symmetries are derivations using the prolongation theorem. Applying the subequation method, we then use the integrating factor property to solve the NLFODE to obtain a few travelling wave solutions to the time FBBM.

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“…us, ψ(x, t) satisfies equation (1). Applying the third prolongation to (1), we have the accompanying deciding condition, which is given as…”

Section: Lie Symmetry and Reduction Of Fbbm Equationmentioning

confidence: 99%

“…Substituting 7and (8) into (16) and equaling coefficients in derivatives for x and power of u to zero, the system of equations is obtained: α 1 xt − η tψ � 0.…”

Section: Lie Symmetry and Reduction Of Fbbm Equationmentioning

confidence: 99%

“…where c 1 and c 2 are constants. By the previous infinitesimal, equation (1) has two vector fields in the form…”

Section: Lie Symmetry and Reduction Of Fbbm Equationmentioning

confidence: 99%