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Using asymptotic methods, one can reduce complicated systems of equations to simpler model equations. The model equation for a single, genuinely nonlinear, hyperbolic wave is Burgers equation. Reducing the gas dynamics equations to a Burgers equation, leads to a theory of nonlinear geometrical acoustics. When diffractive effects are included, the model equation is the ZK or unsteady transonic small disturbance equation. We describe some properties of this equation, and use it to formulate asymptotic equations that describe the transition from regular to Mach reflection for weak shocks. Interacting hyperbolic waves are described by a system of Burgers or ZK equations coupled by integral terms. We use these equations to study the transverse stability of interacting sound waves in gas dynamics.
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 16 | |
popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |