Results 201 to 210 of about 7,864 (230)

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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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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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
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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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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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A Property of the Ansatz of Hirota's Method for Quasilinear Parabolic Equations

Mathematical Notes, 2002
The author deals with the classes of linear fractional solutions to some nonlinear equations. This allows him to construct new solutions for a chosen class of dissipative equations. To construct solutions of a more complicated forms the author proposes to use so-called ``property of zero denominators and factorized brackets''.
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Soliton Stability to the Davey-Stewartson: I. Equation by the Hirota Method

Journal of the Physical Society of Japan, 2001
Summary: The soliton stability of the Davey-Stewartson I equation is discussed by the Hirota method. A close relation exists between the periodic soliton resonance and the soliton instability to the transverse disturbances. It is shown that the solutions of the periodic soliton resonance describe the nonlinear state of the instability.
Tajiri, Masayoshi, Takeuchi, Kiyohiro, Arai, Takahito   +2 more
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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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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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