Ivan Christov and P M Jordan 2008 New J. Phys. 10 043027 doi:10.1088/1367-2630/10/4/043027
Shock bifurcation and emergence of diffusive solitons in a nonlinear wave equation with relaxation
Ivan Christov1 and P M Jordan2
Show affiliationsA hyperbolic generalization of Burgers' equation, which includes relaxation, is examined using analytical and numerical tools. By means of singular surface theory, the evolution of initial discontinuities (i.e. shocks) is fully classified. In addition, the parameter space is explored and the bifurcation experienced by the shock amplitude is identified. Then, by means of numerical simulations based on a Godunov-type scheme, we confirm the theoretical findings and explore the solution structure of a signaling-type initial-boundary-value problem with discontinuous boundary data. In particular, we show that diffusive solitons (or Taylor shocks) can emerge in the solution, behind the wavefront. We also show that, for certain parameter values, a shock wave becomes an acceleration wave in infinite time, an unexpected result that is the exact opposite of the well-known phenomenon of finite-time acceleration wave blow-up. Finally, the 'red light turning green' problem is re-examined.
- PACS
-
02.30.Jr Partial differential equations
02.60.Lj Ordinary and partial differential equations; boundary value problems
- Subjects
- Dates
-
Issue 4 (April 2008)
Received 6 December 2007
Published 15 April 2008
-
Shock bifurcation and emergence of diffusive solitons in a nonlinear wave equation with relaxation
Ivan Christov and P M Jordan 2008 New J. Phys. 10 043027
-
Optical control of a magneto-optical trap for cesium atoms
S Pradhan and B N Jagatap 2007 J. Phys.: Conf. Ser. 80 012041
-
Report on the CCPR Key Comparison K6: Spectral regular transmittance
Gaël Obein and Jean Bastie 2009 Metrologia 46 02002
-
BIPM comparison BIPM.RI(II)-K1.Co-58 of the activity measurements of the radionuclide 58Co and the links for the 2000 regional comparison APMP.RI(II)-K2.Co-58
G Ratel et al 2003 Metrologia 40 06006
-
Superconformal Selfdual σ-Models
Louis Paulot JHEP10(2004)071
-
5D black rings and 4D black holes
Davide Gaiotto et al JHEP02(2006)023
-
FOCUS ON MECHANICAL SYSTEMS AT THE QUANTUM LIMIT
Markus Aspelmeyer and Keith Schwab 2008 New J. Phys. 10 095001
-
Towards efficient generation of attosecond pulses from overdense plasma targets
N M Naumova et al 2008 New J. Phys. 10 025022
-
CO2-assisted embossing for the fabrication of PMMA components under low temperature and with low pressure
Sen-Yeu Yang et al 2008 J. Micromech. Microeng. 18 025024
-
Complementarity in variable strength quantum non-demolition measurements
M Barbieri et al 2009 New J. Phys. 11 093012
Users also read
What's this?- Pulsating–gliding transition in the dynamics of levitating liquid nitrogen droplets
- Confinement of surface state electrons in self-organized Co islands on Au(111)
- Atomic four-wave mixing via condensate collisions
Related review articles
What's this?- Investigation of intermittency and generalized self-similarity of turbulent boundary layers in laboratory and magnetospheric plasmas: towards a quantitative definition of plasma transport features
- Spectral problems in open quantum chaos
- Integral characteristics: a key to understanding structure formation in stochastic dynamic systems