Results 51 to 60 of about 27,126 (206)
The Two Modified G′G‐Expansion Methods for Obtaining Solitons of the Korteweg‐De Vries Equation
Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.The Korteweg‐de Vries (KdV) equation plays an important role in describing the propagation of water waves in shallow channels. Several analytical methods, such as tanh‐function methods (TFMs), exponential function method, and Jacobi elliptic function method, provide the exact solitons to the KdV equation.
Emmanuel Mensah +4 more
wiley +1 more source
Lump Solutions and Interaction Solutions for the Dimensionally Reduced Nonlinear Evolution Equation
Complexity, 2019 In this paper, by means of the Hirota bilinear method, a dimensionally reduced nonlinear evolution equation is investigated. Through its bilinear form, lump solutions are obtained. We construct interaction solutions between lump solutions and one soliton
Baoyong Guo, Huanhe Dong, Yong Fang
doaj +1 more source
Complexity, 2021 In this paper, a generalized (2 + 1)-dimensional Calogero–Bogoyavlenskii–Schiff equation is considered. Based on the Hirota bilinear method, three kinds of exact solutions, soliton solution, breather solutions, and lump solutions, are obtained. Breathers
Hongcai Ma, Qiaoxin Cheng, Aiping Deng
doaj +1 more source
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 +4 more
wiley +1 more source
A search method for Hirota bilinear systems of nonlinear evolution equations
Next ResearchWe present a systematic search method for finding Hirota bilinear systems of nonlinear evolution equations, with emphasis on the nonlinear Schrödinger equation (NLSE). Using a known exact solution, couplings between the different terms of the differential equation are identified, which are then used to derive the bilinear system.
I. Albazlamit +2 more
openaire +2 more sources
Dynamics investigation on a Kadomtsev–Petviashvili equation with variable coefficients
Open Physics, 2022 In this work, we investigate a generalized Kadomtsev–Petviashvili equation with variable coefficients and self-consistent sources in plasma and fluid mechanics.
Peng Li-Juan
doaj +1 more source
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 +5 more
wiley +1 more source
Journal of Function Spaces, Volume 2026, Issue 1, 2026.This manuscript studies the stochastic time fraction modified complex Ginzburg–Landau (SFmCGL) model, an essential dynamical nonlinear model for describing the physical nature of how the optical wave soliton behaves and changes over time in a dynamic optical communication system.
Hala Abd-Elmageed +4 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
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