AI 中文总结
该研究分析二阶正修正伯格斯方程的非局部积分微分流，发现其非局部耗散会打破能量平衡，导致孤波不稳定，无法形成稳定对称的行波。
AI 中文摘要
我们研究修正伯格斯方程通过其标准递归算子生成的高阶流，特别证明二阶正流呈现非局部积分微分方程形式。将方程约化为行波形式后，我们分析其渐近能量行为，结果显示非局部能通量阻止拓扑扭结和钟形孤波的形成。我们还表明，非局部耗散永久打破非线性对流与线性色散间的渐近平衡，造成不可逆能量失衡，分析进一步证实孤波不稳定，非局部项通过辐射引发持续能量损失，致使行波无法维持稳定对称形状。
英文摘要
We study the higher-order flows of the modified Burgers' equation generated by its standard recursion operator. In particular, we show that the second-order positive flow takes the form of a non-local integro-differential equation. After reducing the equation to a traveling-wave form, we investigate its asymptotic energy behavior. The resulting analysis shows that the non-local energy flux prevents the formation of both topological kink and bell-shaped solitary waves. We show that the non-local dissipation permanently breaks the asymptotic equilibrium between nonlinear convection and linear dispersion, forcing an irreversible energy imbalance. Our analysis shows that the solitary waves are unstable. The non-local term causes continuous energy loss through radiation. As a result, the traveling wave cannot keep a stable and symmetric shape.
