Results 151 to 160 of about 6,221 (189)

Soliton Solutions for Nonisospectral AKNS Equation by Hirota's Method

Communications in Theoretical Physics, 2006
Bilinear form of the nonisospectral AKNS equation is given. The N-soliton solutions are obtained through Hirota's method.
Bi Jin-Bo, Sun Ye-Peng, Chen Deng-Yuan
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Application of Hirota's Method to a Perturbed System

Journal of the Physical Society of Japan, 1982
The effect of a perturbation on a solitary wave is studied through an extension of Hirota's method. The same result as those obtained by the ordinary singular perturbation technique and by the perturbation theory of the inverse spectral transform can be more straightforwardly and more easily derived.
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Hirota’s Bilinear Method and Partial Integrability

1990
We discuss Hirota’s bilinear method from the point of view of partial integrability. Many different levels of integrability are shown to exist.
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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.
Xie, Manlin, Ding, Xuanhao
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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
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Dispersive optical solitons with Schrödinger–Hirota model by trial equation method

Optik, 2018
Abstract This paper obtains bright, dark and singular dispersive optical soliton solutions to Schrodinger–Hirota equation by the aid of trial equation method. Both Kerr and power laws of nonlinearity are studied. Singular periodic solutions are also obtained as a byproduct of this scheme.
YAŞAR, EMRULLAH, Belic, Milivoj, Moshokoa, Seithuti P., Alshomrani, Ali Saleh, Zhou, Qin, Yildirim, Yakup, Biswas, Anjan   +6 more
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Neugebauer-Kramer solutions of the Ernst equation in Hirota's direct method

Journal of Physics A: Mathematical and General, 1998
Summary: We prove analytically the Sasa-Satsuma conjecture which states that their solution of bilinear form of the Ernst equation gives the Neugebauere-Kramer solution in particular cases. This proof relates Hirota's direct method with the Bäcklund transformation method and opens the way towards the comprehensive interpretation of the Ernst equation.
Masuda, Tetsu, Sasa, Narimasa, Fukuyama, Takeshi   +2 more
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Hirota bilinear method for nonlinear evolution equations

2003
Summary. The bilinear method introduced by Hirota to obtain exact solutions for nonlinear evolution equations is discussed. Firstly, several examples including the Korteweg-deVries, nonlinear Schrodinger and Toda equations are given to show how solutions are derived.
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Hirota’s Method of Solving Soliton-Type Equations

1978
Although it is a gross oversimplification to say that Hirota’s method amounts to guesswork, this is basically true. It is extremely useful when more sophisticated methods have failed. Its principal drawback (apart from the guesswork element) is that it gives only soliton solutions and no background (or ‘radiation’).
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2 + 1 Dimensional Dromions and Hirota’s Bilinear Method

1991
Hirota’s bilinear formalism is perhaps the best method for constructing solutions of integrable nonlinear evolution equations [1,2]. In this lecture we show how using this method one can easily construct one-dromion solutions for generic equations of nonlinear Schrodinger (n1S) and Korteweg-de Vries (KdV) type [3,4].
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