オガワ　トシユキ   OGAWA Toshiyuki   小川　知之    所属   明治大学  総合数理学部    職種   専任教授
言語種別	日本語
発行・発表の年月	2018/07
形態種別	学術雑誌
査読	査読あり
標題	Rippling rectangular waves for a modified Benney equation
執筆形態	共著(筆頭者)
掲載誌名	Japan Journal of Industrial and Applied Mathematics
掲載区分	国内
巻・号・頁	35,939-968頁
著者・共著者	Tomoyuki Miyaji, Toshiyuki Ogawa, Ayuki Sekisaka
概要	? 2018, The Author(s). One parameter family of rectangular periodic traveling wave solutions are known to exists in a perturbed system of the modified KdV equation. 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.
DOI	10.1007/s13160-018-0304-1
ISSN	09167005
PermalinkURL	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85046737460&origin=inward