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中国物理学会期刊

KdV孤子的含时微扰理论

CSTR: 32037.14.aps.57.1316

Time-dependent perturbation theory of KdV soliton

CSTR: 32037.14.aps.57.1316
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  • 研究了周期性含时微扰对KdV(Korteweg de Vries)孤子的影响. 将微扰项展为时间变量的傅里叶级数,发现其常数项是导致长期项的根源. 在一阶近似下,消除长期项,求出了孤子参数(高度、宽度和速度)随时间的缓慢变化. 傅氏级数中的其他项决定了微扰对孤子波形的一阶修正.

     

    The effects of the periodical time-dependent perturbation on a KdV (Korteweg de Vries) soliton are studied. Expanding the perturbation term into a Fourier series, we find that the time-independent term will lead to the secular terms. In this paper, the soliton parameters (height, width and velocity) are derived by eliminating the secular terms, and the corrections on a soliton caused by perturbation are obtained with the help of other terms in Fourier series in the first-order approximation.

     

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