Results 81 to 90 of about 6,221 (189)

On the New Solutions of the Conformable Time Fractional Generalized Hirota-Satsuma Coupled KdV System

Annals of the West University of Timisoara: Mathematics and Computer Science, 2017
In this paper, generalized Hirota Satsuma coupled KdV system is solved with tanh method and q-Homotopy analysis method. New fractional derivative definition called “conformable fractional derivative” used in the solution procedure.
Çenesiz Yucel, Kurt Ali, Tasbozan Orkun
doaj   +1 more source

Simple Equations Method (SEsM): Algorithm, Connection with Hirota Method, Inverse Scattering Transform Method, and Several Other Methods. [PDF]

Entropy (Basel), 2020
Vitanov NK, Dimitrova ZI, Vitanov KN.
europepmc   +1 more source

Combined Exp-Function Ansatz Method and Applications

Abstract and Applied Analysis, 2013
Our aim is to present a combined Exp-function ansatz method. This method replaces the traditional assumptions of multisolitons by a combination of the hyperbolic functions and triangle functions in Hirota bilinear forms of nonlinear evolution equation ...
Gui Mu, Jun Liu, Zhengde Dai, Xi Liu
doaj   +1 more source

The Hirota direct method

, 2005
Cataloged from PDF version of article. The search for integrability of nonlinear partial differential and difference equations includes the study on multi-soliton solutions. One of the most famous method to construct multi-soliton solutions is the Hirota direct method.
openaire   +1 more source

Numerical simulations for fractional Hirota–Satsuma coupled Korteweg–de Vries systems

Open Physics
In this investigation, the fractional Hirota–Satsuma coupled Korteweg–de Vries (KdV) problem is solved using two modern semi-analytic techniques known as the Aboodh residual power series method (ARPSM) and Aboodh transform iteration method (ATIM).
Ganie Abdul Hamid, Noor Saima, Al Huwayz Maryam, Shafee Ahmad, El-Tantawy Samir A.   +4 more
doaj   +1 more source

A New Method with a Different Auxiliary Equation to Obtain Solitary Wave Solutions for Nonlinear Partial Differential Equations

Advances in Mathematical Physics, 2013
A new method with a different auxiliary equation from the Riccati equation is used for constructing exact travelling wave solutions of nonlinear partial differential equations.
Bülent Kiliç, Hasan Bulut
doaj   +1 more source

Exploring soliton dynamics and wave interactions in an extended Kadomtsev-Petviashvili-Boussinesq equation

Ain Shams Engineering Journal
This research investigates the extended Kadomtsev-Petviashvili-Boussinesq equation, relevant in numerous scenarios involving dissipative media. To initiate the analysis, a Hirota bilinear form is applied, leading to a Bäcklund transformation for the ...
Nauman Raza, Adil Jhangeer, Zeeshan Amjad, Beenish Rani, Dumitru Baleanu   +4 more
doaj   +1 more source

The Conservative Numerical Scheme for the Hirota Equation

Mathematics
In this paper, we derive a semi-discrete scheme using the central difference method, which perfectly preserves the conservation of mass and energy for the Hirota equation.
Jinqi Zhang, Xianggui Li, Dongying Hua
doaj   +1 more source

Exact Solutions of Boussinesq Equations By Hirota Direct Method

Afyon Kocatepe University Journal of Sciences and Engineering
Boussinesq Equations (BSQ) are the focus of this article. First, we provide a basic overview of Hirota's D operator, which is used to build multi-soliton solutions for equations involving nonlinear evolution. After that, some details regarding fourth-order BSQ are provided, and we use Hirota's direct method to find a one-solution solution.
Halide Gümüş, Abdullah Baykal
openaire   +2 more sources

Analytical solutions and chaotic insights into the Hirota-Maccari system. [PDF]

Sci Rep
Usman T, Ullah MS.
europepmc   +1 more source