K（n，n）Rosenau-Hyman方程的耗散扰动
Dissipative perturbations for the K(n,n) Rosenau-Hyman equation
摘要：
紧致子是具有非线性色散的非耗散发展方程的紧支孤波。在应用中，这些模型方程伴随着耗散项，可以被视为小扰动。我们应用绝热微扰的方法来控制的K（n，n）Rosenau-Hyman方程中的耗散项的存在下，保持的“质量”的光子。演化方程的速度和振幅的双光子确定的一些线性和非线性耗散项：第二，第四，第六阶在前一种情况下，和第二和第四阶在后者。该方法的数值验证，提出了一个四阶，线性，耗散扰动，对应于一个奇异摄动项。
英文摘要：
Compactons are compactly supported solitary waves for nondissipative evolution equations with nonlinear dispersion. In applications, these model equations are accompanied by dissipative terms which can be treated as small perturbations. We apply the method of adiabatic perturbations to compactons governed by the K(n,n) Rosenau-Hyman equation in the presence of dissipative terms preserving the "mass" of the compactons. The evolution equations for both the velocity and the amplitude of the compactons are determined for some linear and nonlinear dissipative terms: second-, fourth-, and sixth-order in the former case, and second- and fourth-order in the latter one. The numerical validation of the method is presented for a fourth-order, linear, dissipative perturbation which corresponds to a singular perturbation term.
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