A theoretical study is carried out for bubble oscillation in a compressible liquid with
significant acoustic radiation based on the Keller–Miksis equation using a multi-scaled …

The basic property of thermal runaway is that the temperature blows up at some point in the
domain at a finite time for the appropriate choices of parameters and initial conditions. The …

The long-time viscous decay of large-amplitude bubble oscillations is considered in an
incompressible Newtonian fluid, based on the Rayleigh–Plesset equation. At large …

The asymptotic structure of laminar modulated traveling waves in two-dimensional high-
Reynolds-number plane Poiseuille flow is investigated on the upper-energy branch. A finite …

Original asymptotic solutions are determined for two autonomous differential equations. The
application of initial conditions for the energy, wave number and phase shift proves to be …

The high Reynolds-number structure of the laminar, chaotic and turbulent attractors is
investigated in a two-dimensional Kolmogorov flow. The laminar attractors include the …

Numerical simulations of violent bubble dynamics are often associated with numerical
instabilities at the end of collapse, when a shock wave is emitted. Based on the Keller …

A mathematical model describing the coupling of electrical and optical effects in
semiconductor lasers is introduced. Through a multiple-scale asymptotic expansion, the …

A new mathematical model describing the coupling of electrical, optical and thermal effects
in semiconductor lasers is introduced. The underlying (perfect) isothermal system has a …

Original explicit modulation equations are determined for cnoidal waves of the Korteweg-
deVries (KdV)–Burgers equation. This formal asymptotic analysis is used to demonstrate …