Benney-Luke水波模型中孤立波的渐近稳定性
Asymptotic stability of solitary waves in the Benney-Luke model of water waves
摘要：
本文研究了一维Benney-Luke方程孤立波解的渐近稳定性。对于该方程，与全水波问题一样，由于能量-动量泛函的二次变分是无穷不定的，经典的证明孤立波轨道稳定性的变分方法明显失效。在谱稳定性假设下，证明了非线性系统在能量范数下的稳定性，即线性化不允许非负实部的非零特征值。我们也验证了这一假设的波的小能量。
英文摘要：
We study asymptotic stability of solitary wave solutions in the one-dimensional Benney-Luke equation, a formally valid approximation for describing two-way water wave propagation. For this equation, as for the full water wave problem, the classic variational method for proving orbital stability of solitary waves fails dramatically due to the fact that the second variation of the energy-momentum functional is infinitely indefinite. We establish nonlinear stability in energy norm under the spectral stability hypothesis that the linearization admits no non-zero eigenvalues of non-negative real part. We also verify this hypothesis for waves of small energy.
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