Results 1 to 10 of about 2,945 (146)

Multi-soliton solutions of the Sawada-Kotera equation using the Hirota direct method: Novel insights into nonlinear evolution equations

Partial Differential Equations in Applied Mathematics, 2023
Recently, mathematicians, engineers, and scientists have explored the unique characteristics and potential applications of multi-solitons, which is an expanding domain of study.
A. K. M. Kazi Sazzad Hossain, M. Ali Akbar   +1 more
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Alternative solitons in the Hirota–Satsuma system via the direct method

Partial Differential Equations in Applied Mathematics, 2021
Multisolitons and multi-hump solitons are constructed for the coupled Korteweg–de Vries (cKdV) system introduced by Hirota and Satsuma (1981) in the context of the propagation of two waves interacting with different dispersion relations.
Hugo Parra Prado, Luis A. Cisneros-Ake
doaj   +4 more sources

Painlevé analysis and Hirota direct method for analyzing three novel physical fluid extended KP, Boussinesq, and KP-Boussinesq equations: Multi-solitons/shocks and lumps

Results in Engineering
Due to the extensive and diverse connections of the Kadomtsev-Petviashvili (KP) equation with various physical phenomena, such as the propagation of waves in sea and ocean water and the propagation of nonlinear waves in plasmas when two-dimensional ...
Abdul-Majid Wazwaz, Weaam Alhejaili, R.T. Matoog, Samir A. El-Tantawy   +3 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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On soliton solutions, periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in (2+1) and (3+1) dimensions

Heliyon, 2023
In this paper, the (2+1)-dimensional generalized fifth-order KdV equation and the extended (3+1)-dimensional Jimbo-Miwa equation were transformed into the Hirota bilinear forms with Hirota direct method.
Baoyong Guo, Yong Fang, Huanhe Dong
doaj   +1 more source

Soliton solutions by means of Hirota bilinear forms

Partial Differential Equations in Applied Mathematics, 2022
The paper aims to provide a brief overview of soliton solutions obtained through the Hirota direct method. A bilinear formulation of soliton solutions in both (1+1)-dimensions and (2+1)-dimensions is discussed, together with applications to various ...
Wen-Xiu Ma
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Novel soliton solutions to a (2+1)-dimensional breaking soliton equation

Partial Differential Equations in Applied Mathematics, 2022
In this paper, a Hirota bilinear form is presented for a (2+1)-dimensional breaking soliton equation. Novel N-soliton solutions are constructed through an application of the Hiorta direct method.
Qi Chen, Xiao-ming Zhu, Jian-bing Zhang
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Lump and rogue wave solutions to (1+1)-dimensional evolution equations

Partial Differential Equations in Applied Mathematics, 2022
In this paper, we study lump solutions and rogue wave solutions for three (1+1)-dimensional nonlinear dynamic systems. By applying the Hirota direct method, lump and rogue wave solutions are presented with the aid of symbolic computations.
Yuan Zhou
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New interaction solutions to the (2+1)-dimensional Hirota–Satsuma–Ito equation

Results in Physics, 2022
This study aims to determine novel analytical lump solutions to the (2+1)-dimensional Hirota–Satsuma–Ito equation through conducting symbolic computations using the Hirota direct method.
Fei Long, Shami A.M. Alsallami, S. Rezaei, Kamsing Nonlaopon, E.M. Khalil   +4 more
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Solutions of the Extended Kadomtsev–Petviashvili–Boussinesq Equation by the Hirota Direct Method [PDF]

Journal of Nonlinear Mathematical Physics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +4 more sources