论文标题
较低功率非线性的广义KDV解决方案的动力和动力学
Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity
论文作者
论文摘要
我们考虑了两种类型的广义korteweg -de vries方程，其中非线性给出或没有绝对值，尤其是包括非线性的低功率，其示例为schamel方程。我们首先证明了两个方程式在$ h^1 $的加权子空间中的局部良好性，其中包括具有多项式衰变的功能，将Linares等人[39]的结果扩展到了分数权重。然后，我们通过数值研究解决方案，确认了良好的态度，并将其扩展到包括指数衰减的更广泛的功能。我们包括对两种方程式的解决方案的比较，特别是，我们研究了具有不同衰减速率的正数据和负数据的孤子分辨率。最后，我们研究了两个模型中各种孤立波的相互作用，显示了孤子，色散辐射甚至呼吸器的形成，所有这些都更容易跟踪具有较低功率的非线性。
We consider two types of the generalized Korteweg - de Vries equation, where the nonlinearity is given with or without absolute values, and, in particular, including the low powers of nonlinearity, an example of which is the Schamel equation. We first prove the local well-posedness of both equations in a weighted subspace of $H^1$ that includes functions with polynomial decay, extending the result of Linares et al [39] to fractional weights. We then investigate solutions numerically, confirming the well-posedness and extending it to a wider class of functions that includes exponential decay. We include a comparison of solutions to both types of equations, in particular, we investigate soliton resolution for the positive and negative data with different decay rates. Finally, we study the interaction of various solitary waves in both models, showing the formation of solitons, dispersive radiation and even breathers, all of which are easier to track in nonlinearities with lower power.
