发表机构
Institute of Spectroscopy, Russian Academy of Sciences（俄罗斯科学院光谱学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对正弦-戈登方程，求解Whitham调制方程的单相周期波解，提出自相似解与hodograph解，推广了非线性薛定谔方程系统的相关研究方法，用于描述不稳定性前沿的演化。
AI 中文摘要
找到了满足正弦-戈登方程的单相周期波的Whitham调制方程解，这些解描述了向不稳定区域传播的不稳定性前沿后方振荡区域的演化。一个简单的自相似解描述了由不稳定状态下的局域初始扰动产生的两个不稳定性前沿之间的整个区域，另一个 hodograph 解代表了靠近不稳定性前沿的典型波。该理论推广了此前用于满足非线性薛定谔方程的系统的方法。
英文摘要
Solutions of the Whitham modulation equations for one-phase periodic waves obeying the sine-Gordon equation are found that describe the evolution of an oscillatory region behind an instability front propagating into the instability region. A simple self-similar solution describes the whole region between two fronts of instability resulting from a localized initial disturbance in the unstable state. Another hodograph solution represents typical waves close to the instability fronts. This theory generalizes the approach used previously for systems obeying the nonlinear Schroedinger equation.
Comments9 pages, 7 figures
