Wave equation with a concentrated moving source
A tempered distribution which is an exact solution of the wave equation with a concentrated moving source on the right-hand side, is obtained in the paper by means of the Cagniard - de Hoop method.
Wave fronts to some modifications of Korteweg-de Vries and Burgers-Korteweg-de Vries equations
The existence of a traveling wave with special properties to modified KdV and BKdV equations is proved. Nonlinear terms in the equations are defined by means of a function f of an unknown u satisfying some conditions.
Waves of Autocrine Signaling in Patterned Epithelia
A biophysical model describing long-range cell-to-cell communication by a diffusible signal mediated by autocrine loops in developing epithelia in the presence of a morphogenetic pre-pattern is introduced. Under a number of approximations, the model reduces to a particular kind of bistable reaction-diffusion equation with strong heterogeneity. In the case of the heterogeneity in the form of a long strip a detailed analysis of signal propagation is...
Weak asymptotic method for the study of propagation and interaction of infinitely narrow -solitons.
WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity