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Introduction to the Hirota Direct Method

, 2021
The primary subject matter of the report is the Hirota Direct Method, and the primary goal of the report is to describe and derive the method in detail, and then use it to produce analytic soliton solutions to the Boussinesq equation and the Korteweg-de Vries (KdV) equation.
Capetillo, Pascal, Hornewall, Jonathan
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Exact Solutions of Boussinesq Equations By Hirota Direct Method [PDF]

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
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Diversity of Interaction Solutions of a Shallow Water Wave Equation

Complexity, 2019
In this paper, we study the diversity of interaction solutions of a shallow water wave equation, the generalized Hirota–Satsuma–Ito (gHSI) equation. Using the Hirota direct method, we establish a general theory for the diversity of interaction solutions,
Jian-Ping Yu, Wen-Xiu Ma, Bo Ren, Yong-Li Sun, Chaudry Masood Khalique   +4 more
doaj   +2 more sources

Unification of integrable q-difference equations

Electronic Journal of Differential Equations, 2015
This article presents a unifying framework for q-discrete equations. We introduce a generalized q-difference equation in Hirota bilinear form and develop the associated three-q-soliton solutions which are described in polynomials of power functions ...
Burcu Silindir, Duygu Soyoglu
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Two-Dimensional Toda-Heisenberg Lattice

Symmetry, Integrability and Geometry: Methods and Applications, 2013
We consider a nonlinear model that is a combination of the anisotropic two-dimensional classical Heisenberg and Toda-like lattices. In the framework of the Hirota direct approach, we present the field equations of this model as a bilinear system, which ...
Vadim E. Vekslerchik
doaj   +1 more source

Dispersive Quiescent Optical Solitons with DWDM Topology

AppliedMath
The paper retrieves quiescent dispersive solitons in dispersion-flattened optical fibers having nonlinear chromatic dispersion and the Kerr law of self-phase modulation. The platform model is the Schrödinger–Hirota equation. The enhanced direct algebraic
Elsayed M. E. Zayed, Mona El-Shater, Ahmed H. Arnous, Lina S. Calucag, Anjan Biswas   +4 more
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Geometrical representation and Hirota direct approach for multiple soliton solutions of nonlinear M-coupled fractional equations

Mathematical and Computer Modelling of Dynamical Systems
This paper introduces a novel analytical framework for deriving multiple soliton and singular soliton solutions to M-coupled fractional evolution equations.
Abaker A. Hassaballa, Mehmet Yavuz, Emad A.-B. Abdel-Salam, Gassan A.M.O. Farah, Ibtisam Daqqa   +4 more
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SOLITON SOLUTIONS OF THE GENERALIZED NONLINEAR SCHR?DINGER EQUATION WITH HIGHER-ORDER CORRECTIONS BY THE DIRECT METHOD OF HIROTA

Acta Physica Sinica, 1991
By using the direct method of Hirota, explicit multi-soliton solutions are found for the generalized nonlinear Schr?dinger equation with higherorder corrections which describes the ultra-short pulse propagation along monomode optical fibers.
null LIU ZHONG-ZHU, null HUANG NIAN-NING
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Resonant soliton molecules, asymmetric solitons and the other diverse wave solutions to the (3 + 1)-dimensional generalized Kudryashov-Sinelshchikov equation for liquid with gas bubbles

Results in Physics
Under the present study, we focus on developing some exact solutions of the (3 + 1)-dimensional generalized Kudryashov-Sinelshchikov equation (KSE) for the liquid with gas bubbles.
Peng Xu, Huan Huang, Chun Shan, Kang-Jia Wang   +3 more
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Application of Hirota's Direct Method to Nonlinear Partial Differential Equations: Bilinear Form and Soliton Solutions

, 2022
The Hirota method to get the soliton solutions for a nonlinear partial differential equation is the mostefficient direct technique researchers use worldwide. This article reviews and explores Hirota’s directtechnique on the KdV equation, which Hirota initially used to clarify his method.
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