Results 51 to 60 of about 1,434 (182)

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

Relations for zeros of special polynomials associated to the Painleve equations

, 2006
A method for finding relations for the roots of polynomials is presented. Our approach allows us to get a number of relations for the zeros of the classical polynomials and for the roots of special polynomials associated with rational solutions of the ...
Ablowitz, Ahmed, Amdeberhan, Bassom, Calogero, Clarkson, Clarkson, Clarkson, Clarkson, Clarkson, Conte, Cosgrove, Demina, Demina, Hone, Iwasaki, Jrad, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Maria V. Demina, Mugan, Nikolai A. Kudryashov, Okamoto, Pickering, Stieltjes, Stieltjes, Szego, Umemura, Veselov, Vorob'ev, Yablonskii   +36 more
core   +1 more source

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

New exact solutions of the Mikhailov-Novikov-Wang equation via three novel techniques

Journal of Ocean Engineering and Science, 2023
The current work aims to present abundant families of the exact solutions of Mikhailov-Novikov-Wang equation via three different techniques. The adopted methods are generalized Kudryashov method (GKM), exponential rational function method (ERFM), and ...
Arzu Akbulut, Melike Kaplan, Mohammed K.A. Kaabar   +2 more
doaj   +1 more source

Explicit expressions for meromorphic solution of autonomous nonlinear ordinary differential equations

, 2011
Meromorphic solutions of autonomous nonlinear ordinary differential equations are studied. An algorithm for constructing meromorphic solutions in explicit form is presented.
Eremenko, Hone, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Lavrent’ev, Malfliet, Maria V. Demina, Nevanlinna, Nikolay A. Kudryashov, Parkes, Sikorsky, Vernov, Vernov   +21 more
core   +1 more source

Investigation of Dark and Bright Soliton Solutions of Some Nonlinear Evolution Equations

ITM Web of Conferences, 2018
In this paper, generalized Kudryashov method (GKM) is used to find the exact solutions of (1+1) dimensional nonlinear Ostrovsky equation and (4+1) dimensional Fokas equation. Firstly, we get dark and bright soliton solutions of these equations using GKM.
Demiray Seyma Tuluce, Bulut Hasan
doaj   +1 more source

Exact solutions of equations for the Burgers hierarchy

, 2011
Some classes of the rational, periodic and solitary wave solutions for the Burgers hierarchy are presented.
Benton, Burgers, Cole, Dmitry I. Sinelshchikov, Fahmy, Gudkov, Heremant, Hopf, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Malfliet, Nikolai A. Kudryashov, Olver, Polyanin, Rosenblatt, Shanga, Wang, Wazwaz, Weiss, Yang   +23 more
core   +1 more source

Analytical and Numerical Soliton Solutions of the Shynaray II‐A Equation Using the G′G,1G$$ \left(\frac{G^{\prime }}{G},\frac{1}{G}\right) $$‐Expansion Method and Regularization‐Based Neural Networks

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq, H. W. A. Riaz, Sadique Rehman, M. Mamun Miah, Wen Xiu Ma   +4 more
wiley   +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

Postural control in humans: a study using transcutaneous spinal cord stimulation

Experimental Physiology, Volume 111, Issue 4, Page 2163-2175, 1 April 2026.
Abstract The aim of the study was to investigate the spinal mechanisms involved in regulating postural balance in humans. Participants stood in a normal stance, with their spinal postural networks either non‐invasively activated or not stimulated by electrical stimulation.
Natalia Shamantseva, Ivan Sakun, Tatiana Klishkovskaia, Andrey Aksenov, Vsevolod Lyakhovetskii, Tatiana Moshonkina   +5 more
wiley   +1 more source