2018年7月1日

# Rippling rectangular waves for a modified Benney equation

Japan Journal of Industrial and Applied Mathematics
• Tomoyuki Miyaji
• ,
• Toshiyuki Ogawa
• ,
• Ayuki Sekisaka

35
2

939

968

DOI
10.1007/s13160-018-0304-1

© 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.

リンク情報
DOI
https://doi.org/10.1007/s13160-018-0304-1
Scopus
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