A new class of exact solutions of the Vlasov equation

2001 ◽  
Vol 8 (12) ◽  
pp. 5081-5085 ◽  
Author(s):  
M. Y. Yu ◽  
Zhaoyang Chen ◽  
L. Stenflo
Keyword(s):  
Exact Solutions ◽  
Vlasov Equation ◽  
New Class

GEOMETRIC INTEGRATION BY SOLUTION INTERPOLATION

2009 ◽  
Vol 20 (02) ◽  
pp. 313-322
Author(s):  
PILWON KIM
Keyword(s):  
Differential Equation ◽  
Heat Equation ◽  
Exact Solutions ◽  
Standard Method ◽  
Interpolation Method ◽  
Nonlinear Heat Equation ◽  
Geometric Integration ◽  
Numerical Schemes ◽  
New Class ◽  
Geometric Integrators

Numerical schemes that are implemented by interpolation of exact solutions to a differential equation naturally preserve geometric properties of the differential equation. The solution interpolation method can be used for development of a new class of geometric integrators, which generally show better performances than standard method both quantitatively and qualitatively. Several examples including a linear convection equation and a nonlinear heat equation are included.

New class of exact solutions of the Dirac equation

1975 ◽  
Vol 16 (10) ◽  
pp. 2089-2092 ◽  
Author(s):  
Franklin S. Felber ◽  
John H. Marburger
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
New Class

Complete model of a self-gravitating cosmic string: A new class of exact solutions

1995 ◽  
Vol 52 (10) ◽  
pp. 5588-5597 ◽  
Author(s):  
Charles C. Dyer ◽  
Francine R. Marleau
Keyword(s):  
Exact Solutions ◽  
Cosmic String ◽  
Complete Model ◽  
New Class

scholarly journals New class of exact solutions in string theory

1995 ◽  
Vol 51 (6) ◽  
pp. 2896-2917 ◽  
Author(s):  
Gary T. Horowitz ◽  
A. A. Tseytlin
Keyword(s):  
String Theory ◽  
Exact Solutions ◽  
New Class

scholarly journals Symmetries and exact solutions of the rotating shallow-water equations

2009 ◽  
Vol 20 (5) ◽  
pp. 461-477 ◽  
Author(s):  
A. A. CHESNOKOV
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
New Class ◽  
New Exact Solutions ◽  
Time Periodic Solutions ◽  
Rotating Shallow Water ◽  
Rotating Shallow Water Equations ◽  
Time Periodic

Lie symmetry analysis is applied to study the non-linear rotating shallow-water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow-water equations can be transformed to the classical shallow-water model. The derived symmetries are used to generate new exact solutions of the rotating shallow-water equations. In particular, a new class of time-periodic solutions with quasi-closed particle trajectories is constructed and studied. The symmetry reduction method is also used to obtain some invariant solutions of the model. Examples of these solutions are presented with a brief physical interpretation.

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