Riemann problem and wave interactions for the one-dimensional relativistic string equation in Minkowski space

2020 ◽  
Vol 486 (2) ◽  
pp. 123932
Author(s):  
Jianli Liu ◽  
Ruixi Liu
Keyword(s):  
Minkowski Space ◽  
Riemann Problem ◽  
Relativistic String ◽  
String Equation ◽  
Wave Interactions ◽  
One Dimensional ◽  
The One

Bifurcation diagrams and exact multiplicity of positive solutions of one-dimensional prescribed mean curvature equation in Minkowski space

2019 ◽  
Vol 21 (03) ◽  
pp. 1850003 ◽  
Author(s):  
Xuemei Zhang ◽  
Meiqiang Feng
Keyword(s):  
Minkowski Space ◽  
Mean Curvature ◽  
Bifurcation Diagrams ◽  
One Dimensional ◽  
Curvature Equation ◽  
Prescribed Mean Curvature ◽  
Mean Curvature Equation ◽  
Prescribed Mean Curvature Equation ◽  
The One ◽  
Exact Multiplicity

In this paper, bifurcation diagrams and exact multiplicity of positive solution are obtained for the one-dimensional prescribed mean curvature equation in Minkowski space in the form of [Formula: see text] where [Formula: see text] is a bifurcation parameter, [Formula: see text], the radius of the one-dimensional ball [Formula: see text], is an evolution parameter. Moreover, we make a comparison between the bifurcation diagram of one-dimensional prescribed mean curvature equation in Euclid space and Minkowski space. Our methods are based on a detailed analysis of time maps.

scholarly journals Implicit and time reversible CABARET schemes for quasilinear shallow water equations

2016 ◽  
pp. 402-414
Author(s):  
В.М. Головизнин ◽  
Д.Ю. Горбачев ◽  
А.М. Колокольников ◽  
П.А. Майоров ◽  
П.А. Майоров ◽  
...  
Keyword(s):  
Difference Scheme ◽  
Numerical Solution ◽  
Shallow Water ◽  
Riemann Problem ◽  
Shallow Water Equations ◽  
Unconditionally Stable ◽  
One Dimensional ◽  
Dispersion Properties ◽  
The One ◽  
Stable Scheme

Предложена новая неявная безусловно устойчивая схема для одномерных уравнений мелкой воды, сохраняющая все особенности явной схемы Кабаре. Проведен анализ диссипативных и дисперсионных свойств новой схемы и предложен алгоритм ее численного решения. Приведены примеры решения задачи о распаде разрыва. A new implicit unconditionally stable scheme for the one-dimensional shallow water equations is proposed. This implicit scheme retains all the features of the explicit CABARET (Compact Accurately Boundary Adjusting-REsolution Technique) difference scheme. Dissipative and dispersion properties of this new scheme are analyzed; an algorithm of its numerical solution is discussed. Some examples of solving the Riemann problem are considered.

scholarly journals Whitham modulation theory for the Kadomtsev– Petviashvili equation

2017 ◽  
Vol 473 (2204) ◽  
pp. 20160695 ◽  
Author(s):  
Mark J. Ablowitz ◽  
Gino Biondini ◽  
Qiao Wang
Keyword(s):  
Linear Stability ◽  
Riemann Problem ◽  
Vries Equation ◽  
Complete Integrability ◽  
Kp Equation ◽  
One Dimensional ◽  
Stability Properties ◽  
Petviashvili Equation ◽  
Modulation Theory ◽  
The One

The genus-1 Kadomtsev–Petviashvili (KP)-Whitham system is derived for both variants of the KP equation; namely the KPI and KPII equations. The basic properties of the KP-Whitham system, including symmetries, exact reductions and its possible complete integrability, together with the appropriate generalization of the one-dimensional Riemann problem for the Korteweg–de Vries equation are discussed. Finally, the KP-Whitham system is used to study the linear stability properties of the genus-1 solutions of the KPI and KPII equations; it is shown that all genus-1 solutions of KPI are linearly unstable, while all genus-1 solutions of KPII are linearly stable within the context of Whitham theory.

scholarly journals A-topology for Minkowski space

1979 ◽  
Vol 21 (1) ◽  
pp. 53-64 ◽  
Author(s):  
Sribatsa Nanda
Keyword(s):  
Minkowski Space ◽  
Dimensional Space ◽  
Three Dimensional ◽  
One Dimensional ◽  
Group Of Homeomorphisms ◽  
Dimensional Space Time ◽  
The One ◽  
Induced Topology ◽  
Time Continuum ◽  
Inhomogeneous Lorentz Group

AbstractWe consider in this paper a topology (which we call the A-topology) on Minkowski space, the four-dimensional space–time continuum of special relativity and derive its group of homeomorphisms. We define the A-topology to be the finest topology on Minkowski space with respect to which the induced topology on time-like and light-like lines is one-dimensional Euclidean and the induced topology on space-like hyperplanes is three- dimensional Euclidean. It is then shown that the group of homeomorphisms of this topology is precisely the one generated by the inhomogeneous Lorentz group and the dilatations.

scholarly journals Delta Shock Wave for the Suliciu Relaxation System

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Richard De la cruz ◽  
Juan Galvis ◽  
Juan Carlos Juajibioy ◽  
Leonardo Rendón
Keyword(s):  
Riemann Problem ◽  
Entropy Condition ◽  
Delta Shock Wave ◽  
One Dimensional ◽  
Hugoniot Relation ◽  
Delta Shock ◽  
The Cauchy Problem ◽  
The One ◽  
Linearly Degenerate ◽  
Characteristic Field

We study the one-dimensional Riemann problem for a hyperbolic system of three conservation laws of Temple class. This system is a simplification of a recently proposed system of five conservations laws by Bouchut and Boyaval that model viscoelastic fluids. An important issue is that the considered3×3system is such that every characteristic field is linearly degenerate. We show an explicit solution for the Cauchy problem with initial data inL∞. We also study the Riemann problem for this system. Under suitable generalized Rankine-Hugoniot relation and entropy condition, both existence and uniqueness of particular delta-shock type solutions are established.

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