A generalization of the Korteweg-de Vries equation (KdVE) is considered in which additional
terms belonging to the Kuramoto-Sivashinsky equation (KSE) are incorporated to account …

We consider a thin layer of a viscous fluid flowing down a uniformly heated planar wall. The
heating generates a temperature distribution on the free surface which in turn induces …

We first summarize features of free, forced and stochastic harmonic oscillations and,
following an idea first proposed by Lord Rayleigh in 1883, we discuss the possibility of …

In recent years there has been growing interest in the study of the nonlinear spatio-temporal
dynamics of problems appearing in various? elds of science and engineering. In a wide …

The existence of a solitary wave for the shallow water model in convecting circumstance was
established in previous works. It is still unknown that whether there exist periodic waves. In …

An overview is given of recent results about the onset and development of steady and time–
dependent flow motions past an instability threshold induced by the Marangoni effect. First, I …

A dissipation-modified Boussinesq-like system of equations governing three-dimensional
long wavelength Marangoni-Bénard oscillatory convection in a shallow layer heated from …

We consider two-dimensional stationary solitary pulses in a falling film by using the two-
dimensional generalized Kuramoto-Sivashinsky equation as a model system. We …

The longwave instabilities are inherent to a variety of systems in fluid dynamics (from
dynamics of atmosphere and ocean to motion in microfluidic devices), geophysics (mantle …

В монографии рассматривается широкий круг задач, связанных с локализацией
нелинейных волн деформации в средах и волноводах. Представлена асимптотическая …