Results 161 to 170 of about 6,361 (199)

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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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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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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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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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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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’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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The Hirota Method and Soliton Solutions to the Multidimensional Nonlinear Schrodinger Equation

Siberian Mathematical Journal, 2002
By using the Hirota method the author finds one-soliton solutions to the generalized \(3+1\) nonlinear Schrödinger equation \[ i \psi_t = \psi_{xy} + \psi_{xz} + V \psi, \qquad V_x = 2((|\psi|^2)_y + (|\psi|^2)_z) \] derived by R. Myrzakulov. Notice that in the variables \(x, \eta = (y+z)/2, \xi = (y-z)/2\) this system takes the following \(2+1\) form:
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New ways of applying the Hirota method in soliton theory

1996
info:eu-repo/semantics ...
Loris, Ignace, Lambert, Franklin, Willox, R.   +2 more
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