Results 61 to 70 of about 11,033,514 (203)

Multistructure Novel Stochastic Soliton Solutions for the (2+1)‐Dimensional Breaking Wave Equation Within the Fractional Derivative Influence

Complexity, Volume 2026, Issue 1, 2026.
In this paper, we investigate the exact stochastic solutions of the (2 + 1)‐dimensional stochastic fractional‐space breaking soliton equation (SFSBSE) involving the truncated M‐fractional derivative in space. This equation models a range of physical phenomena, including fluid wave propagation, shallow water dynamics, and plasma physics, under the ...
Fatma Nur Kaya Sağlam, Volkan Ala, Bahadır Kopçasız, Ercan Çelik, Lingzhong Guo   +4 more
wiley   +1 more source

Bifurcation, Chaotic Behavior, Sensitivity Analysis, and Traveling Wave Solutions of the Nonlinear Telecommunication Model Through Transmission Lines

Discrete Dynamics in Nature and Society, Volume 2026, Issue 1, 2026.
This paper explores a nonlinear telecommunication transmission line model with the incorporation of the M‐truncated fractional derivative, providing memory‐dependent effects that go beyond the classical nonlinear transmission line models. The Hamilton–Jacobi and Jacobian dynamical frameworks are, for the first time, utilized in this fractional ...
Arooma Zainab, Muhammad Abbas, Y. S. Hamed, Asnake Birhanu, Tahir Nazir, Muhammad Zain Yousaf, Sundarapandian Vaidyanathan   +6 more
wiley   +1 more source

Periodic wave solutions of nonlinear equations by Hirota's bilinear method

, 2006
31pages ...
Dai, H. H., Geng, E. G. Fan X. G.
openaire   +2 more sources

A novel and efficient method for obtaining Hirota’s bilinear form for the nonlinear evolution equation in (n+1) dimensions

Partial Differential Equations in Applied Mathematics, 2022
Bilinearization of nonlinear partial differential equations (PDEs) is essential in the Hirota method, which is a widely used and robust mathematical tool for finding soliton solutions of nonlinear PDEs in a variety of fields, including nonlinear dynamics, mathematical physics, and engineering sciences.
Sachin Kumar, Brij Mohan
openaire   +2 more sources

A Symmetry‐Compatible Auxiliary‐Field Splitting of the Korteweg–de Vries Equation: Exact Linearisation via the Direct and Inverse Pathways

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
This paper introduces a symmetry‐compatible exact linearisation of the Korteweg–de Vries (KdV) equation through an auxiliary‐field splitting based on Q = νfx. The term ‘symmetry’ is used here in a structural sense; the linear operator is held fixed across solution families, rather than in the sense of Lie point symmetry groups.
Jorge Rodolfo Silva Zabadal, Claudio Zen Petersen, Vinicius Gadis Ribeiro, Ederson Staudt, Huaiqin Wu   +4 more
wiley   +1 more source

Constructing various wave symmetries on the blood flow and arterial wall motion model using the Hirota bilinear method

Results in Engineering
In this research, the Hirota bilinear method is used for the development and examination of different types of wave symmetries of a blood flow and arterial wall motion model.
Baboucarr Ceesay, Nauman Ahmed, Muhammad Zafarullah Baber, Zafar Iqbal, Ali Akgül   +4 more
doaj   +1 more source

New Types of Doubly Periodic Standing Wave Solutions for the Coupled Higgs Field Equation

Abstract and Applied Analysis, 2014
Based on the Hirota bilinear method and theta function identities, we obtain a new type of doubly periodic standing wave solutions for a coupled Higgs field equation.
Gui-qiong Xu
doaj   +1 more source

A (2+1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solutions

Nuclear Physics B, 2020
In this paper, a (2+1)-dimensional sine-Gordon equation and a sinh-Gordon equation are derived from the well-known AKNS system. Based on the Hirota bilinear method and Lie symmetry analysis, kink wave solutions and traveling wave solutions of the (2+1 ...
Gangwei Wang, Kaitong Yang, Haicheng Gu, Fei Guan, A.H. Kara   +4 more
doaj   +1 more source

Exploring Advanced Soliton Solutions for the Stochastic Nonlinear System With Temporal Fractionality: Multiplicative Noise Intensity, Modulation Instability, and Chaotic Nature

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
This study investigates the stochastic fractional new coupled Konno–Oono equation with external forced multiplicative noise, focusing on the chaotic nature, the influence of multiplicative noise intensity, and the fractionality parameter on exact soliton solutions. The proposed model is used to describe the complex phenomena in the magnetic field.
Md. Mamunur Roshid, Ramy M. Hafez, Mahtab Uddin, Yakup Yildirim, Golam Mostafa, Zuo Da-Wei   +5 more
wiley   +1 more source

Localized coherent structures of Ishimori equation I through Hirota’s bilinearization method: Time dependent/stationary boundaries [PDF]

Chaos, Solitons & Fractals, 2007
Ishimori equation is a $(2+1)$ dimensional generalization of the $(1+1)$ dimensional integrable classical continuous Heisenberg ferromagnetic spin equation. The richness of the coherent structures admitted by Ishimori equation I such as dromion, lump and rationally- exponentially localized solutions, have been demonstrated in the literature through ...
Vijayalakshmi, S., Lakshmanan, M.
openaire   +2 more sources