Chowdury A, Kedziora D J, Ankiewicz A, Akhmediev N
Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Sep;90(3):032922. doi: 10.1103/PhysRevE.90.032922. Epub 2014 Sep 26.
We present the fifth-order equation of the nonlinear Schrödinger hierarchy. This integrable partial differential equation contains fifth-order dispersion and nonlinear terms related to it. We present the Lax pair and use Darboux transformations to derive exact expressions for the most representative soliton solutions. This set includes two-soliton collisions and the degenerate case of the two-soliton solution, as well as beating structures composed of two or three solitons. Ultimately, the new quintic operator and the terms it adds to the standard nonlinear Schrödinger equation (NLSE) are found to primarily affect the velocity of solutions, with complicated flow-on effects. Furthermore, we present a new structure, composed of coincident equal-amplitude solitons, which cannot exist for the standard NLSE.
我们给出了非线性薛定谔层级的五阶方程。这个可积偏微分方程包含五阶色散及其相关的非线性项。我们给出了拉克斯对，并使用达布变换来推导最具代表性的孤子解的精确表达式。这组解包括双孤子碰撞以及双孤子解的简并情况，还有由两个或三个孤子组成的拍频结构。最终发现，新的五次算子及其添加到标准非线性薛定谔方程（NLSE）中的项主要影响解的速度，并产生复杂的后续效应。此外，我们还给出了一种由重合等幅孤子组成的新结构，而标准NLSE不存在这种结构。
