"Rippling rectangular waves for a modified Benney equation"
Mathematics, Mechanics, and Materials Unit (Fried Unit) would like to invite you to a Seminar by Prof. Toshiyuki Ogawa, Meiji University in Tokyo.
Date: Friday, October 20, 2017
Venue: C015, Level C, Lab1
Professor Toshiyuki Ogawa
Meiji University, Tokyo
Rippling rectangular waves for a modified Benney equation
One parameter family of rectangular periodic traveling wave solutions are known to exists in a perturbed system of the modified KdV equation which was obtained from the traffic jam model. The rectangular periodic traveling wave consists basically of front and back transitions. It turns out that the rectangular traveling wave becomes unstable as its period becomes large. More precisely, torus bifurcation occurs successively along the branch of the rectangular traveling wave solutions. And, as a result, a ``rippling rectangular wave'' appears. It is roughly the rectangular traveling wave on which small pulse wave trains are superimposed. The bifurcation branch is constructed by a numerical torus continuation method. The instability is explained by using the accumulation of eigenvalues on the essential spectrum around the stationary solutions. Moreover, the critical eigenfunctions which correspond to the torus bifurcation can be characterized theoretically. This talk is based on the joint work between Tomoyuki Miyaji and Ayuki Sekisaka both in Meiji University.