扰动Korteweg-de Vries方程的Whitham理论
Whitham theory for perturbed Korteweg-de Vries equation
摘要：
原始的Whitham的调制方程的推导方法适用于系统的动态描述的扰动Korteweg-de Vries方程。区分两种情况：（i）扰动导致调制方程中出现右手边，使得它们变得不均匀;（ii）扰动导致修改Whitham速度矩阵。得到了每种情况下Whitham调制方程的一般形式。通过一个所谓的“广义Korteweg-de Vries方程”的例子说明了它们之间的本质区别。在耗散扰动的情况下，考虑了求扰动Whitham方程定态解的方法。
英文摘要：
Original Whitham's method of derivation of modulation equations is applied to systems whose dynamics is described by a perturbed Korteweg-de Vries equation. Two situations are distinguished: (i) the perturbation leads to appearance of right-hand sides in the modulation equations so that they become non-uniform; (ii) the perturbation leads to modification of the matrix of Whitham velocities. General form of Whitham modulation equations is obtained for each case. The essential difference between them is illustrated by an example of so-called `generalized Korteweg-de Vries equation'. Method of finding steady-state solutions of perturbed Whitham equations in the case of dissipative perturbations is considered.
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