Ginzburg-Landau方程中的脉冲和蛇
Pulses and Snakes in Ginzburg--Landau Equation
摘要：
利用偏微分方程的变分形式，结合常微分方程的数值模拟，我们发现了两类（脉冲和蛇）耗散孤子，并分析了它们的形状和稳定性对五阶Ginzburg-Landau方程（CGLE）物理参数的依赖关系.在过去的三十年里，在许多可积和非可积系统中研究了规则孤波，与此相反，这些耗散孤波在时间上是不稳定的。相反，它们是空间受限的脉冲型结构，其包络表现出复杂的时间动态。数值模拟显示了非常有趣的分岔序列的参数的CGLE的变化。我们的预测的孤子的振幅，宽度，位置，速度和相位的变化的解决方案，使用变分公式与模拟结果一致。
英文摘要：
Using a variational formulation for partial differential equations (PDEs) combined with numerical simulations on ordinary differential equations (ODEs), we find two categories (pulses and snakes) of dissipative solitons, and analyze the dependence of both their shape and stability on the physical parameters of the cubic-quintic Ginzburg-Landau equation (CGLE). In contrast to the regular solitary waves investigated in numerous integrable and non-integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are spatially confined pulse-type structures whose envelopes exhibit complicated temporal dynamics. Numerical simulations reveal very interesting bifurcations sequences as the parameters of the CGLE are varied. Our predictions on the variation of the soliton amplitude, width, position, speed and phase of the solutions using the variational formulation agree with simulation results.
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