Results 41 to 50 of about 1,413 (195)

Symmetric and asymmetric binary-solitons to the generalized two-mode KdV equation: Novel findings for arbitrary nonlinearity and dispersion parameters

Results in Physics, 2023
In this paper, the two-mode version of the generalized KdV (gTMKdV) equation is presented. The new model arises in weakly dispersive and nonlinear wave medium and describes the motion of either symmetric or asymmetric binary-waves regarding each wave’s ...
Mohammed Ali, Marwan Alquran, Abdallah BaniKhalid   +2 more
doaj   +1 more source

Observations on the tanh-coth expansion method for finding solutions to nonlinear evolution equations [PDF]

, 2010
The 'tanh-coth expansion method' for finding solitary travelling-wave solutions to nonlinear evolution equations has been used extensively in the literature. It is a natural extension to the basic tanh-function expansion method which was developed in the
Parkes, E.J.
core   +1 more source

Stable Optical Solitons for the Higher-Order Non-Kerr NLSE via the Modified Simple Equation Method

Mathematics, 2021
This paper studies the propagation of the short pulse optics model governed by the higher-order nonlinear Schrödinger equation (NLSE) with non-Kerr nonlinearity.
Noha M. Rasheed, Mohammed O. Al-Amr, Emad A. Az-Zo’bi, Mohammad A. Tashtoush, Lanre Akinyemi   +4 more
doaj   +1 more source

Some analytic and series solutions of integrable generalized Broer-Kaup system

Alexandria Engineering Journal, 2022
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 integrability of the model. Then,
Sandeep Malik, Sachin Kumar, Pinki Kumari, Kottakkaran Sooppy Nisar   +3 more
doaj   +1 more source

Extended equation for description of nonlinear waves in liquid with gas bubbles

, 2013
Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves.
Kudryashov, Nikolai A., Sinelshchikov, Dmitry I.   +1 more
core   +1 more source

The Functional Expansion Approach for Solving NPDEs as a Generalization of the Kudryashov and G′/G Methods

Symmetry, 2022
This paper presents the functional expansion approach as a generalized method for finding traveling wave solutions of various nonlinear partial differential equations. The approach can be seen as a combination of the Kudryashov and G′/G solving methods. It allowed the extension of the first method to the use of second order auxiliary equations, and, at
Carmen Ionescu, Corina N. Babalic, Radu Constantinescu, Raluca Efrem   +3 more
openaire   +2 more sources

On elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equation

, 2006
The Conte-Musette method has been modified for the search of only elliptic solutions to systems of differential equations. A key idea of this a priory restriction is to simplify calculations by means of the use of a few Laurent series solutions instead ...
Ablowitz M J, Buchberger B, Buchberger B, Conte R, Davenport J, Drouffe J-M, Erdélyi A, Eremenko A E, Fan E, Fan E, Gerdt V P, Ginzburg V L, Hone A N W, Kudryashov N A, Kudryashov N A, Kudryashov N A, Kudryashov N A, Kudryashov N A, Kudryashov N A Demina M V, Landau L D, Nikitin A G Barannyk T A, Porubov A V, S Yu Vernov, Tabor M, Timoshkova E I, Timoshkova E I, Vernov S Yu, Vernov S Yu, Vernov S Yu Ganzha V G Mayr E W Vorozhtsov E V, von Hurwitz A   +29 more
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Optical soliton solutions of (1 + 1)- and (2 + 1)-dimensional generalized Sasa–Satsuma equations using new Kudryashov method

International Journal of Geometric Methods in Modern Physics, 2022
In this paper, we aim to derive new soliton solutions of (1+1)- and (2+1)-dimensional generalized Sasa–Satsuma equations via the new Kudryashov method. In optical fiber transmission systems, the Sasa–Satsuma equation describes the effects of third-order dispersion, self-steepening and stimulated Raman scattering in the propagation of ultrafast pulses.
Melih Cinar, Aydin Secer, Muslum Ozisik, Mustafa Bayram   +3 more
openaire   +4 more sources

Meromorphic exact solutions of the generalized Bretherton equation

, 2011
The generalized Bretherton equation is studied. The classification of the meromorphic traveling wave solutions for this equation is presented.
Abramowitz, Biswas, Demina, Demina, Dmitry I. Sinelshchikov, Eremenko, Hone, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Maria V. Demina, Nikolai A. Kudryashov, Parkes, Parkes, Vernov, Vitanov   +20 more
core   +1 more source

Some more bounded and singular pulses of a generalized scale-invariant analogue of the Korteweg–de Vries equation

Results in Physics, 2023
We investigate a generalized scale-invariant analogue of the Korteweg–de Vries (KdV) equation, establishing a connection with the recently discovered short-wave intermediate dispersive variable (SIdV) equation.
Sayed Saifullah, M.M. Alqarni, Shabir Ahmad, Dumitru Baleanu, Meraj Ali Khan, Emad E. Mahmoud   +5 more
doaj   +1 more source