3 papers
nlin.PS2017
Universal behavior of modulationally unstable media
Gino Biondini, Sitai Li, Dionyssis Mantzavinos +1
Evidence is presented of universal behavior in modulationally unstable media. An ensemble of nonlinear evolution equations, including three partial differential equations, an integ…
math.AP2017
Revisiting Diffusion: Self-similar Solutions and the Decay in Initial and Initial-Boundary Value Problems
P. G. Kevrekidis, M. O. Williams, D. Mantzavinos +3
The diffusion equation is a universal and standard textbook model for partial differential equations (PDEs). In this work, we revisit its solutions, seeking, in particular, self-si…
math.AP2011
The Kadomtsev-Petviashvili I Equation on the Half-Plane
Dionyssios Mantzavinos, Athanassios S. Fokas
A new method for the solution of initial-boundary value problems for \textit{linear} and \textit{integrable nonlinear} evolution PDEs in one spatial dimension was introduced by one…