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Some exact solutions of the Yu�Toda�Sasa�Fukuyama equation with time-dependent coefficients via two different methods
(Elsevier B.V., 2022-09-06)
In the current study, the generalized (G?/G)-expansion method and a new modified simple equation method (NMSEM) have been utilized to secure the exact solutions of the Yu-Toda-Sasa-Fukuyama (YTSF) equation with time-dependent ...
Soliton Solutions of�Dual-mode Kawahara Equation via�Lie Symmetry Analysis
(Springer Science and Business Media Deutschland GmbH, 2022-06-29)
In this article, we investigate a newly proposed dual-mode Kawahara equation. Our main aim in this paper is to find out the soliton and periodic solutions of the Kawahara equation. Initially, we reduce the governing equation ...
Highly dispersive W�shaped and other optical solitons with quadratic�cubic nonlinearity: Symmetry analysis and new Kudryashov's method
(Elsevier Ltd, 2023-06-24)
Lie symmetry analysis is utilized in this paper to explore the properties of highly dispersive optical solitons that exhibit quadratic�cubic self-phase modulation. The use of Lie symmetry analysis enables the reduction of ...
The integrable Boussinesq equation and it�s breather, lump and soliton solutions
(Springer Science and Business Media B.V., 2022-01-17)
The fourth-order nonlinear Boussinesq water wave equation, which explains the propagation of long waves in shallow water, is explored in this article. We used the Lie symmetry approach to analyze the Lie symmetries and ...
A (2+1)-dimensional combined KdV�mKdV equation: integrability, stability analysis and soliton solutions
(Springer Science and Business Media B.V., 2022-01-10)
In this study, the (2+1)-dimensional combined Korteweg�de Vries and modified Korteweg�de Vries equation has been considered for the first time. Firstly, we check the integrability of the governing equation. Then, we generate ...
Some analytic and series solutions of integrable generalized Broer-Kaup system
(Elsevier B.V., 2022-01-03)
In this article, we have updated the results obtained by Zhang et al. (2019) and derived some certain features of a famous dispersion water wave model, namely, generalized Broer-Kaup (BK) system. First, we have shown the ...
Cubic-Quartic Optical Solitons in Fiber Bragg Gratings with Dispersive Reflectivity Having Parabolic Law of Nonlinear Refractive Index by Lie Symmetry
(MDPI, 2022-11-11)
This work recovers cubic-quartic optical solitons with dispersive reflectivity in fiber Bragg gratings and parabolic law of nonlinearity. The Lie symmetry analysis first reduces the governing partial differential equations ...
A generalized (2+1)-dimensional Hirota bilinear equation: integrability, solitons and invariant solutions
(Springer Science and Business Media B.V., 2022-11-11)
In this paper, we consider an extended form of generalized (2 + 1) -dimensional Hirota bilinear equation which demonstrates nonlinear wave phenomena in shallow water, oceanography and nonlinear optics. We have successfully ...
Application of new Kudryashov method to various nonlinear partial differential equations
(Springer, 2022-11-13)
The purpose of this work is to seek various innovative exact solutions using the new Kudryashov approach to the nonlinear partial differential equations (NLPDEs). This technique obtains novel exact solutions of soliton ...
Some exact solitons to the (2 + 1)-dimensional Broer�Kaup�Kupershmidt system with two different methods
(Springer, 2023-10-21)
The exact solutions of the (2 + 1) dimensional Broer�Kaup�Kupershmidt (BKK) system which has been recommended to model the nonlinear and dispersive long gravity waves traveling along with the two horizontal directions in ...