Results 201 to 210 of about 6,812 (242)

Internal symmetries of soliton equations

Physica Scripta, 1991
Summary: The geometrical structure of integrable nonlinear evolution equations is related to a conformal symmetry group acting in the space of solutions. This internal symmetry is shown to result from the interplay between Bäcklund transformations and Darboux transformations of the Lax pair.
Stahlhofen, A. A., Schramm, A. J.
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Hypergeometric Solutions of Soliton Equations

Theoretical and Mathematical Physics, 2001
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Orlov, A. Yu., Scherbin, D. M.
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On the Geometry of Soliton Equations

Acta Applicandae Mathematicae, 1995
This is an interesting survey paper on the bi-Hamiltonian approach to soliton equations. No previous knowledge of soliton equations is required to study the present paper, which can be particularly useful to graduate students who are seeking to enter the subject.
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Spatial solitons of Maxwell’s equations

Optics Letters, 1994
Spatial solitons of Maxwell's equations propagating in an isotropic Kerr material differ significantly from the classical soliton of the nonlinear Schrödinger equation unless the electric field is linearly polarized along a geometric axis of the soliton intensity pattern.
A W, Snyder, D J, Mitchell, Y, Chen
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Solitons and singular solitons for the Gardner–KP equation

Applied Mathematics and Computation, 2008
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Attactors of dissipative soliton equation

Applied Mathematics and Mechanics, 1994
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Tian, Lixin, Xu, Zhenyuan, Liu, Zhengrong   +2 more
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Solitons of a Nonlinear Schrödinger Equation

1980
In recent years, there has been a considerable development in the study of the soliton solutions of the class of nonlinear Schrodinger equations (1) for several forms of the nonlinear term F(ρ ...
MINELLI T. A., PASCOLINI, ALESSANDRO
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The exploding solitons of the sine–Gordon equation

Applied Mathematics Letters
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Shuzhi Liu, Deqin Qiu
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The geometry of soliton equations.

1988
From the MR review by R.Schmid: "Ideas from the geometrical study of soliton equations are used to give an explanation of some algorithmic procedures used in the field of the inverse scattering technique (IST). In the first three sections particular classes of manifolds are introduced: Poisson manifolds, Poisson-Nijenhuis manifolds and GN manifolds ...
MAGRI F, MOROSI C, TONDO, GIORGIO SALVATORE   +2 more
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Bilinearization of Soliton Equations

Journal of the Physical Society of Japan, 1982
Transformations of soliton equations into the bilinear forms involving four dependent variables are discussed. It is found that both nonlinear Schrodinger equation and classical Heisenberg ferromagnet equation are transformed into the same bilinear from, while the equation \begin{aligned} \phi_{xt}{=}\phi(1-|\phi_{t}|^{2})^{1/2} \end{aligned} shares ...
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