Results 141 to 150 of about 6,221 (189)

A simplified hirota method and its application

Journal of Shanghai University (English Edition), 2003
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Xu, Guiqiong, Zhang, Shanqing, Li, Zhibin   +2 more
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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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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.
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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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Investigation of Hirota equation: Modified double Laplace decomposition method

Physica Scripta, 2021
Abstract In this article, the non-linear coupled Hirota equations are considered attributed to localized excitations. By employing a modified double Laplace transform decomposition method, we derived the general approximate solutions for the coupled Hirota and coupled Hirota Satsuma equations.
Khalid Khan, Zareen Khan, Amir Ali, Muhammad Irfan   +3 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
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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, Yu-Zhen Chai, Hui-Qin Hao
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Hirota's Method and the Singular Manifold Expansion

Journal of the Physical Society of Japan, 1987
A system of equations u t +( u 2 /2-α u m x +β u n x ) x =0 ( m , n : positive integers, β≠0) is studied by means of Hirota's method and the singular manifold expansion. The singular manifold expansion yields the transformation of the system into bilinear forms or higher order ones and we obtain some explicit solutions of the system in physically ...
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The Infinite-Line Hirota Method

2010
Publisher Summary This chapter discusses the infinite-line Hirota method. The Hirota direct method is developed to study soliton solutions and integrability in nonlinear wave equations. This approach provided an alternative theoretical tool for attacking soliton equations.
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Complexiton solutions to soliton equations by the Hirota method

Journal of Mathematical Physics, 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 theory is used to construct multi-complexion solutions to the Korteweg–de Vries equation.
Yuan Zhou, Wen-Xiu Ma
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