Travelling wave solutions to a perturbed Korteweg-de Vries equation
Travelling wave solutions to a perturbed Korteweg-de Vries equation
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DOI：
10.32917/hmj/1206128032
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发表时间：
1994
影响因子：
0.2
通讯作者：
T. Ogawa
中科院分区：
文献类型：
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作者：
T. Ogawa
这里，假定波动仅取决于平面的梯度方向x。变量u表示波在点x和时间t的高度。物理参数α，β和y都是正数。让我们假设斜面朝着x的方向无限长，即xe(-oo，oo)。则(1.1)可以通过对u、x和t进行适当的尺度变换而被认为是一个单参数方程。例如，(1.1)可以变换为以下ε方程系列：
Here, the wave motion is assumed to depend only on the gradient direction x of the plane. The variable u means the height of the wave at the point x and time t. The physical parameters α, β and y are all positive. Let us assume that the inclined plane is infinitely long toward the direction of x, that is, xe(— oo, oo). Then (1.1) can be considered as a 1-parameter equation by taking an appropriate scale transformation of u, x and t. For example, (1.1) can be transformed to the following ε-family of equations: