Shock Wave Solutions of the Einstein Equations: A General Theory with Examples

2001 ◽  
pp. 105-258 ◽  
Author(s):  
Joel Smoller ◽  
Blake Temple
Keyword(s):  
Shock Wave ◽  
General Theory ◽  
Einstein Equations ◽  
Wave Solutions

Astrophysical shock-wave solutions of the Einstein equations

1995 ◽  
Vol 51 (6) ◽  
pp. 2733-2743 ◽  
Author(s):  
Joel Smoller ◽  
Blake Temple
Keyword(s):  
Shock Wave ◽  
Einstein Equations ◽  
Wave Solutions

scholarly journals Nematic Dispersive Shock Waves from Nonlocal to Local

2021 ◽  
Vol 11 (11) ◽  
pp. 4736
Author(s):  
Saleh Baqer ◽  
Dimitrios J. Frantzeskakis ◽  
Theodoros P. Horikis ◽  
Côme Houdeville ◽  
Timothy R. Marchant ◽  
...  
Keyword(s):  
Shock Wave ◽  
Liquid Crystals ◽  
Shock Waves ◽  
Numerical Solutions ◽  
Wave Structure ◽  
Beam Power ◽  
Input Beam ◽  
Shock Wave Structure ◽  
Wave Solutions ◽  
Modulation Theory

The structure of optical dispersive shock waves in nematic liquid crystals is investigated as the power of the optical beam is varied, with six regimes identified, which complements previous work pertinent to low power beams only. It is found that the dispersive shock wave structure depends critically on the input beam power. In addition, it is known that nematic dispersive shock waves are resonant and the structure of this resonance is also critically dependent on the beam power. Whitham modulation theory is used to find solutions for the six regimes with the existence intervals for each identified. These dispersive shock wave solutions are compared with full numerical solutions of the nematic equations, and excellent agreement is found.

scholarly journals Vacuum solutions of Einstein equations that depend on one coordinate

2020 ◽  
pp. 10-11
Author(s):  
S. Parnovsky
Keyword(s):  
Exact Solution ◽  
General Theory ◽  
Cosmological Constant ◽  
Gravitational Wave ◽  
Einstein Equations ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Vacuum Metrics ◽  
Vacuum Solutions ◽  
Zero Frequency

In the famous textbook written by Landau and Lifshitz all the vacuum metrics of the general theory of relativity are derived, which depend on one coordinate in the absence of a cosmological constant. Unfortunately, when considering these solutions the authors missed some of the possible solutions discussed in this article. An exact solution is demonstrated, which is absent in the book by Landau and Lifshitz. It describes space-time with a gravitational wave of zero frequency. It is shown that there are no other solutions of this type than listed above and Minkowski’s metrics. The list of vacuum metrics that depend on one coordinate is not complete without solution provided in this paper.

scholarly journals Diversity of Interaction Solutions of a Shallow Water Wave Equation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Jian-Ping Yu ◽  
Wen-Xiu Ma ◽  
Bo Ren ◽  
Yong-Li Sun ◽  
Chaudry Masood Khalique
Keyword(s):  
Fluid Dynamics ◽  
Wave Equation ◽  
General Theory ◽  
Shallow Water ◽  
Water Wave ◽  
Direct Method ◽  
Soliton Solutions ◽  
Interaction Solutions ◽  
Shallow Water Wave ◽  
Wave Solutions

In this paper, we study the diversity of interaction solutions of a shallow water wave equation, the generalized Hirota–Satsuma–Ito (gHSI) equation. Using the Hirota direct method, we establish a general theory for the diversity of interaction solutions, which can be applied to generate many important solutions, such as lumps and lump-soliton solutions. This is an interesting feature of this research. In addition, we prove this new model is integrable in Painlevé sense. Finally, the diversity of interactive wave solutions of the gHSI is graphically displayed by selecting specific parameters. All the obtained results can be applied to the research of fluid dynamics.

Shock wave solutions of the variants of the Kadomtsev–Petviashvili equation

2011 ◽  
Vol 89 (9) ◽  
pp. 979-984 ◽  
Author(s):  
Houria Triki ◽  
B.J.M. Sturdevant ◽  
T. Hayat ◽  
O.M. Aldossary ◽  
A. Biswas
Keyword(s):  
Shock Wave ◽  
Wave Solution ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Shock Wave Solution

This study obtained the shock wave or kink solutions of the variants of the Kadomtsev–Petviashvili equation with generalized evolution. There are three types of variants of this equation that were considered. The relation between the parameters and the constraint conditions will naturally fall out as a consequence of the derivation of the shock wave solution.

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