Results 181 to 190 of about 48,721 (216)

Multiple-soliton solutions of Einstein’s equations

Journal of Mathematical Physics, 1989
Using the Belinsky–Zakharov generating technique and a flat metric as a seed, two- and four-soliton solutions of the Einstein vacuum equations for the cases of stationary axisymmetric, cylindrically symmetric, or plane symmetric gravitational fields are considered. Three- and five-parameter classes of exact solutions are obtained, some of which are new.
Economou, A., Tsoubelis, D.
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Integrable mappings and soliton equations II

Physica D: Nonlinear Phenomena, 1989
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Quispel, G. R. W., Roberts, J. A. G., Thompson, C. J.   +2 more
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Geometrization of soliton equations

Physics Letters A, 1979
Abstract A unified geometric picture of the soliton equations is presented. All the soliton equations in 1 + 1 dimensions that can be solved by the inverse scattering methods (e.g. sine-Gordon, Korteweg-de Vries and modified Korteweg-de Vries equations) are shown to describe pseudospherical surfaces, i.e.
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Other Ubiquitous Soliton Equations

2003
In the previous chapter, we have seen that the KdV equation is a completely integrable, infinite-dimensional, nonlinear dynamical system. It possesses exact soliton solutions exhibiting remarkable particle-like collision properties. Its Cauchy initial value problem is completely solvable through the Inverse Scattering Transform (IST) procedure by ...
M. Lakshmanan, S. Rajasekar
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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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Soliton and Algebraic Equation

Journal of the Physical Society of Japan, 1982
The close relationship between the soliton and the algebraic equation is found in the case of the Benjamin-Ono equation. Many interesting formulas are presented concerning the algebra of the zeros of the Laguerre polynomial.
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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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The Classical Soliton Equations

2003
Abstract An exciting development in nonlinear science during the 1970s was the gradual realization that certain nonlinear partial differential equations display a variety of exact solutions. These include not only solitary waves-known since the nineteenth century studies of Russell, Bazin, and Boussinesq—but solutions involving an ...
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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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Soliton Solution of Good Boussinesq Equation

Vietnam Journal of Mathematics, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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