Results 61 to 70 of about 2,053 (172)

The Painlev\'e methods

, 2002
This short review is an introduction to a great variety of methods, the collection of which is called the Painlev\'e analysis, intended at producing all kinds of exact (as opposed to perturbative) results on nonlinear equations, whether ordinary, partial,
Conte, Robert, Musette, Micheline
core   +1 more source

The analysis of the traveling wave solutions of the Hirota-Ramani equation via the modified Kudryashov method

AIMS Mathematics
In this paper, the modified Kudryashov method is utilized to construct the exact traveling solutions to the Hirota­-Ramani equation. The Hirota-Ramani equation holds significant importance as a fundamental model in the examination of nonlinear and integrable systems.
Aslı Alkan, Mehmet Kayalar, Hasan Bulut
openaire   +2 more sources

On the Dispersive Optical Pulses in Fiber Optics of the Conformable (2 + 1)‐Dimensional Hirota–Maccari System

Journal of Mathematics, Volume 2026, Issue 1, 2026.
The Hirota–Maccari (HM) system is a fundamental model in wave propagation that has been widely utilized to investigate complex nonlinear phenomena in nonlinear optics, optical communications, and mathematical physics. The HM system sheds light on critical insights into soliton dynamics, wave interactions, and other nonlinear effects.
Fei Li, Mesut Balibey, Shafqat Ur Rehman, Muhammad Bilal, Smritijit Sen   +4 more
wiley   +1 more source

Novel explicit breath wave and numerical solutions of an Atangana conformable fractional Lotka–Volterra model

Alexandria Engineering Journal, 2021
This research studies novel analytical solutions of an Atangana conformable fractional Lotka–Volterra (LV) model system arising in ecology by means of three systematic schemes (the extended simplest equation method, modified Kudryashov method, and the ...
Mostafa M.A. Khater, Mohamed S. Mohamed, Hammad Alotaibi, M.A. El-Shorbagy, S.H. Alfalqi, J.F. Alzaidi, Dianchen Lu   +6 more
doaj   +1 more source

Three-Period Orbits in Billiards on the Surfaces of Constant Curvature

, 2011
An approach due to Wojtkovski [9], based on the Jacobi fields, is applied to study sets of 3-period orbits in billiards on hyperbolic plane and on two-dimensional sphere. It is found that the set of 3-period orbits in billiards on hyperbolic plane, as in
Blumen, Victoria, Kim, Ki Yeun, Nance, Joe, Zharnitsky, Vadim   +3 more
core   +3 more sources

The Dynamical Landscape of the Negative‐Order (3+1)‐Dimensional Calogero–Bogoyavlenskii–Schiff Equation

Journal of Mathematics, Volume 2026, Issue 1, 2026.
A new negative‐order form of the (3 + 1)‐dimensional Calogero–Bogoyavlenskii–Schiff equation is examined in this investigation. This equation plays an important role in accurately describing the thermodynamic properties of mixtures, particularly in chemical engineering applications.
Ulviye Demirbilek, Jan Muhammad, Arzu Akbulut, Usman Younas, Taha Radwan, Karim K. Ahmed, Dimitri Mugnai   +6 more
wiley   +1 more source

Structure of Analytical and Numerical Wave Solutions for the Nonlinear (1 + 1)-Coupled Drinfel’d–Sokolov–Wilson System Arising in Shallow Water Waves

Mathematics, 2023
In this article, we successfully obtain novel solutions for the coupled Drinfel’d–Sokolov–Wilson DSW system utilizing various methods. These include soliton solutions characterized by hyperbolic, rational, and trigonometric functions.
Sumayah Hamzah Alhejaili, Abdulghani Alharbi   +1 more
doaj   +1 more source

On Modified Method of Simplest Equation for Obtaining Exact Solutions of Nonlinear PDEs: Case of Elliptic Simplest Equation [PDF]

, 2012
2010 Mathematics Subject Classification: 74J30, 34L30.The modified method of simplest equation is useful tool for obtaining exact and approximate solutions of nonlinear PDEs.
K. Vitanov, Nikolay
core  

B\"acklund transformations for the second Painlev\'e hierarchy: a modified truncation approach

, 1998
The second Painlev\'e hierarchy is defined as the hierarchy of ordinary differential equations obtained by similarity reduction from the modified Korteweg-de Vries hierarchy. Its first member is the well-known second Painlev\'e equation, P2.
Ablowitz M J, Ablowitz M J, Ablowitz M J, Ablowitz M J, Airault H, Albrecht D W, Andrew Pickering, Bassom A P, Chazy J, Flaschka H, Fokas A S, Fordy A P, Gambier B, Gibbon J D, Gordoa P R, Gromak V I, Ince E L, Its A R, Kudryashov N A, Lax P D, Nalini Joshi, Painlevé P, Painlevé P, Peter A Clarkson, Weiss J, Weiss J   +25 more
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Exploring the Chavy–Waddy–Kolokolnikov Model: Analytical Study via Recently Developed Techniques

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This work explores the analytical soliton solutions to the Chavy–Waddy–Kolokolnikov equation (CWKE), which is a well‐known equation in biology that shows how light‐attracted bacteria move together. This equation is very useful for analyzing pattern creation, instability regimes, and minor changes in linear situations since bacterial movement is very ...
Jan Muhammad, David Yaro, Usman Younas, Chang Phang   +3 more
wiley   +1 more source