论文标题
非线性Schrodinger方程的单数孤子分子
Singular Soliton Molecules of the Nonlinear Schrodinger Equation
论文作者
论文摘要
我们使用Darboux转换方法为局部非线性Schrödinger方程（NLSE）提供了精确的解决方案。新解决方案描述了两个溶剂分子的轮廓和动力学。使用代数销售种子溶液，我们获得了带有不同峰的两氧化溶液，我们将其表示为单一的单人物分子。我们发现新溶液具有有限的结合能。我们计算两个孤子之间的相互作用的力和潜力，这些孤子子是分子类型的。还验证了两个孤子之间键的稳健性。此外，我们使用相同的方法和种子溶液获得了非局部NLSE的新解决方案。在这种情况下，新解决方案对应于孤子的弹性碰撞，平坦背景上的呼吸孤子以及带有线性坡道的背景上的呼吸孤子。最后，我们考虑了一个在时间上而不是空间的NLSE。尽管我们没有找到该方程式的松弛对，但我们得出了三个精确的解决方案。
We derive an exact solution to the local nonlinear Schrödinger equation (NLSE) using the Darboux transformation method. The new solution describes the profile and dynamics of a two-soliton molecule. Using an algebraically-decaying seed solution, we obtain a two-soliton solution with diverging peaks, which we denote as singular soliton molecule. We find that the new solution has a finite binding energy. We calculate the force and potential of interaction between the two solitons, which turn out to be of molecular-type. The robustness of the bond between the two solitons is also verified. Furthermore, we obtain a new solution to the nonlocal NLSE using the same method and seed solution. The new solution in this case corresponds to an elastic collision of a soliton, a breather soliton on flat background, and a breather soliton on a background with linear ramp. Finally, we consider an NLSE which is nonlocal in time rather than space. Although we did not find a Lax pair to this equation, we derive three exact solutions.
