Rippling rectangular waves for a modified Benney equation
Rippling rectangular waves for a modified Benney equation
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修正本尼方程的波纹矩形波
DOI：
10.1007/s13160-018-0304-1
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发表时间：
2018
影响因子：
0.9
通讯作者：
Sekisaka Ayuki
中科院分区：
文献类型：
--
作者：
Miyaji Tomoyuki;Ogawa Toshiyuki;Sekisaka Ayuki
已知在修正KdV方程的摄动系统中存在一个参数族的矩形周期行波解。矩形周期行波主要由前后跃迁组成。结果表明，矩形行波随着周期的增大而变得不稳定。更准确地说，环面分岔是沿着矩形行波解的分支连续发生的。结果，出现了“波纹矩形波”。它大致是叠加了小脉冲波列的矩形行波。采用数值环面延拓法构造分叉分支。利用稳态解周围特征谱上特征值的累积来解释不稳定性。此外，还可以从理论上刻画出环面分岔对应的临界特征函数。
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.