Results 61 to 70 of about 697 (208)
Journal of Mathematics, Volume 2026, Issue 1, 2026.This study presents the dynamic analysis of stochastic fractional unstable nonlinear Schrödinger equation (SFuNLSE), focusing on the analysis of bifurcation, chaotic nature, return map, recurrence plots, strange attractor, basin attractor, power spectrum, chaotic nature and also finds the exact optical soliton solution with multiplicative noise ...
Md. Mamunur Roshid +3 more
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Periodic wave solutions of nonlinear equations by Hirota's bilinear method
, 2006 31pages ...
Dai, H. H., Geng, E. G. Fan X. G.
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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
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Complexiton solutions to soliton equations by the Hirota method
, 2017 We apply the Hirota direct method to construct complexiton solutions (complexitons). The key is to use Hirota bilinear forms. We prove that taking pairs of conjugate wave variables in the 2N-soliton solutions generates N-complexion solutions. The general
Yuan Zhou +3 more
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Journal of Mathematics, Volume 2026, Issue 1, 2026.To investigate the fractional coupled Wu‐Zhang system analytically, this paper uses a hybrid generalized Riccati−Bernoulli sub‐ODE scheme and Bäcklund transformation to find the exact kink, antikink, and bright‐kink soliton solutions. The dynamical properties of these solutions are discussed using Hamiltonian formulation, phase‐portrait analysis, and ...
M. Mossa Al-Sawalha +2 more
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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.
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Results in Physics, 2023 Many two-place physical problems can be explicitly presented as related events model named Alice–Bob systems. In this paper, an integrable Alice–Bob Boussinesq system is introduced via the Boussinesq equation with parameters, which may meet the symmetry transformation of Psˆx (parity with a shift) and Tdˆt (time reversal with a delay).
Li-Hong Jiang +3 more
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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
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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 +4 more
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Non classical interaction aspects to a nonlinear physical model
Results in Physics, 2023 This study deals the dynamics of waves to the conformable fractional (2+1)-dimensional Nizhnik–Novikov–Veselov (NNV) equations. The (2+1)-dimensional NNV equations are the isotropic Lax integrable extension of the (1+1)-dimensional Korteweg–de Vries ...
Hajar F. Ismael +5 more
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