scholarly journals Two-soliton solutions of relativistic field equations

1978 ◽  
Vol 60 (3) ◽  
pp. 269-276 ◽  
Author(s):  
O. Steinmann
Keyword(s):  
Soliton Solutions ◽  
Field Equations ◽  
Relativistic Field

scholarly journals Soliton solutions in relativistic field theories and gravitation

2008 ◽  
Vol 30 ◽  
pp. 193-196
Author(s):  
J. Diaz-Alonso ◽  
D. Rubiera-Garcia
Keyword(s):  
Soliton Solutions ◽  
Field Theories ◽  
Relativistic Field

The Bianchi Identities in the Generalized Theory of Gravitation

1950 ◽  
Vol 2 ◽  
pp. 120-128 ◽  
Author(s):  
A. Einstein
Keyword(s):  
General Principle ◽  
Field Structure ◽  
Field Equations ◽  
Relativistic Field ◽  
Bianchi Identities ◽  
Principle Of Relativity ◽  
Dependent Variables ◽  
Physical Validity ◽  
Theory Of Gravitation

1. General remarks. The heuristic strength of the general principle of relativity lies in the fact that it considerably reduces the number of imaginable sets of field equations; the field equations must be covariant with respect to all continuous transformations of the four coordinates. But the problem becomes mathematically well-defined only if we have postulated the dependent variables which are to occur in the equations, and their transformation properties (field-structure). But even if we have chosen the field-structure (in such a way that there exist sufficiently strong relativistic field-equations), the principle of relativity does not determine the field-equations uniquely. The principle of “logical simplicity” must be added (which, however, cannot be formulated in a non-arbitrary way). Only then do we have a definite theory whose physical validity can be tested a posteriori.

Exact soliton solutions for a class of coupled field equations

1993 ◽  
Vol 173 (1) ◽  
pp. 30-32 ◽  
Author(s):  
Xin-Yi Wang ◽  
Bing-Chang Xu ◽  
Philip L. Taylor
Keyword(s):  
Soliton Solutions ◽  
Field Equations ◽  
Coupled Field ◽  
Coupled Field Equations ◽  
Exact Soliton Solutions

Integrable and solvable systems, and relations among them

1985 ◽  
Vol 315 (1533) ◽  
pp. 451-457 ◽  
Keyword(s):  
Gordon Equation ◽  
Soliton Solutions ◽  
The Self ◽  
Sine Gordon Equation ◽  
Field Equations ◽  
Four Dimensions ◽  
Painlevé Property ◽  
All Solutions ◽  
Special Cases ◽  
Integrable Dynamical Systems

There are several different classes of differential equations that may be described as ‘integrable’ or ‘solvable’. For example, there are completely integrable dynamical systems; equations such as the sine—Gordon equation, which admit soliton solutions; and the self-dual gauge-field equations in four dimensions (with generalizations in arbitrarily large dimension). This lecture discusses two ideas that link all of these together: one is the Painlevé property, which says (roughly speaking) that all solutions to the equations are meromorphic; the other is that many of the equations are special cases (i.e. reductions) of others.

On the exact soliton solutions for a class of coupled field equations

1993 ◽  
Vol 182 (2-3) ◽  
pp. 300-301 ◽  
Author(s):  
Xiaowu Huang ◽  
Jiahua Han ◽  
Kaiyi Qian ◽  
Wei Qian
Keyword(s):  
Soliton Solutions ◽  
Field Equations ◽  
Coupled Field ◽  
Coupled Field Equations ◽  
Exact Soliton Solutions

scholarly journals Component Minimization of the Bargmann?Wigner Wavefunction

1978 ◽  
Vol 31 (2) ◽  
pp. 137 ◽  
Author(s):  
EA Jeffery
Keyword(s):  
Arbitrary Spin ◽  
Spin Operator ◽  
The Other ◽  
Operator Matrices ◽  
Field Equations ◽  
Relativistic Field

The Bargmann-Wigner equations are used to derive relativistic field equations with only 2(2j+ 1) components of the original wavefunction. The other components of the Bargmann-Wigner wavefunction are superfluous and can be defined in terms of the 2(2j+ 1) components. The results are compared with various 2(2j+ 1) theories in the literature. Sylvester's theorem and some properties of induced matrices give simple relationships between the operator matrices of the field equations and the arbitrary spin operator matrices.

Double-Alekseev inverse scattering method in the stationary axi-symmetric vacuum gravitation field equations

Open Physics ◽  
2008 ◽  
Vol 6 (3) ◽  
Author(s):  
Chun-Yan Wang ◽  
Yuan-Xing Gui ◽  
Ya-Jun Gao
Keyword(s):  
Inverse Scattering ◽  
Function Method ◽  
Complex Function ◽  
Soliton Solutions ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Field Equations ◽  
Double Complex ◽  
Gravitation Field ◽  
Symmetric Vacuum

AbstractWe present a new improvement to the Alekseev inverse scattering method. This improved inverse scattering method is extended to a double form, followed by the generation of some new solutions of the double-complex Kinnersley equations. As the double-complex function method contains the Kramer-Neugebauer substitution and analytic continuation, a pair of real gravitation soliton solutions of the Einstein’s field equations can be obtained from a double N-soliton solution. In the case of the flat Minkowski space background solution, the general formulas of the new solutions are presented.

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