Results 151 to 160 of about 6,361 (199)

Multi-soliton solutions and Breathers for the generalized coupled nonlinear Hirota equations via the Hirota method

Superlattices and Microstructures, 2017
Abstract Under investigation in this paper is the generalized coupled nonlinear Hirota (GCH) equations with addition effects by the Hirota method, which is better than the coupled nonlinear Schrodinger equations in eliciting optical solitons for increasing the bit rates.
Ting-Ting Jia
exaly   +2 more sources

∂̄-Dressing method for a generalized Hirota equation

International Journal of Modern Physics B, 2022
Based on a [Formula: see text] matrix [Formula: see text] problem, we have obtained the Lax pair by constructing a spectral transformation matrix. The Hirota equation with self-consistent sources is derived by considering the nonanalytic part of the dispersion relation.
Yehui Huang, Jingjing Di, Yuqin Yao
openaire   +1 more source

The Painlevé Property and Hirota's Method

Studies in Applied Mathematics, 1985
The connection between the Painlevé property for partial differential equations, proposed by Weiss, Tabor, and Carnevale, and Hirota's method for calculating N‐soliton solutions is investigated for a variety of equations including the nonlinear Schrödinger and mKdV equations.
Gibbon, J. D., Radmore, P., Tabor, M., Wood, David Harlan   +3 more
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A simplified hirota method and its application

Journal of Shanghai University (English Edition), 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xu, Guiqiong, Zhang, Shanqing, Li, Zhibin   +2 more
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Hirota’s Method and the Painlevé Property

1985
Given a system of nonlinear ordinary or partial differential equations a most challenging problem is to find an analytical test to determine whether the given system is integrable. In the case of systems of o.d.e’s integrability (in the classical sense of “integration by quadratures” [1]) requires one to find as many integrals of the motion as the ...
J. D. Gibbon, M. Tabor
openaire   +1 more source

Derivation of monopole solutions by Hirota's method

Journal of Physics A: Mathematical and General, 1988
Summary: The second-order field equations in the 't Hooft-Polyakov monopole theory in the Prasad-Sommerfield limit are solved by Hirota's method. All the known point and regular solutions are rederived in a systematic way.
Ajithkumar, C. M., Sabir, M.
openaire   +1 more source

Stability Analysis of a Soliton by the Hirota Method

Journal of the Physical Society of Japan, 1988
The Hirota bilinear method is applied to a weakly perturbed system and the stability of the soliton with respect to the bending of wavefront is studied. This method is more useful for stability analysis than the ordinary perturbation method or the perturbation treatment of the inverse scattering method.
Michiaki Matsukawa, Shinsuke Watanabe, Hiroshi Tanaca   +2 more
openaire   +1 more source

Hirota's Bilinear Method and its Generalization

International Journal of Modern Physics A, 1997
We review Hirota's bilinear method for constructing multisoliton solutions, its use in searching for new soliton equations, and its generalization to higher multi-linearity using gauge invariance as the determining property. Hirota's method is relevant even when a soliton solution is not the object of the study, as an example we show how it clarifies ...
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A Higher-Dimensional Hirota Condition and Its Judging Method

Communications in Theoretical Physics, 2008
Summary: When a one-dimensional nonlinear evolution equation could be transformed into a bilinear differential form as \(F(D_tD_x)f\cdot f = 0\), Hirota proposed a condition for the above evolution equation to have arbitrary N-soliton solutions, we call it the 1-dimensional Hirota condition. As far as higher-dimensional nonlinear evolution equations go,
Guo, Fu-Kui, Zhang, Yu-Feng
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A new method for a generalized Hirota–Satsuma coupled KdV equation

Applied Mathematics and Computation, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Manlin Xie, Xuanhao Ding
openaire   +1 more source