Results 121 to 130 of about 7,864 (230)

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

Finding the one-loop soliton solution of the short-pulse equation by means of the homotopy analysis method

, 2009
The homotopy analysis method is applied to the short-pulse equation in order to find an analytic approximation to the known exact solitary upright-loop solution. It is demonstrated that the approximate solution agrees well with the exact solution.
Abbasbandy, S., Parkes, E.J.
core   +1 more source

Hirota bilinear forms of evolution type equations and their interaction solutions

, 2023
Bu tez çalışmasında bazı oluşum tipi denklemlerin Hirota metodu ile tam çözümlerinin elde edilmesi araştırılmıştır. Bu anlamda Hirota bilineer formuna sahip olan yeni bir (3+1)-boyutlu oluşum tipi modelin çeşitli fiziksel özellikleri haiz olan tam ...
Zeynel, Melih
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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

The Hirota direct method

, 2016
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. In this thesis, we explain this method in detail and apply it to explicit examples.
openaire   +1 more source

Optical solitons, complexitons, Gaussian soliton and power series solutions of a generalized Hirota equation

, 2018
In this paper, we consider a generalized Hirota equation with a bounded potential, which can be used to describe the propagation properties of optical soliton solutions.
Jin-Jin Mao, Tian-Tian Zhang, Li Zou, Shou-Fu Tian   +3 more
core   +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

Hirota equation and Bethe ansatz

, 1998
The paper is a review of recent works devoted to analysis of classical integrable structures in quantum integrable models solved by one or another version of the Bethe ansatz.
A. Zabrodin
core