论文标题
在非线性系统中搜索缺失的d'AlemberT波：Nizhnik-Novikov-Veselov方程
Searching for missing D'Alembert waves in nonlinear system: Nizhnik-Novikov-Veselov equation
论文作者
论文摘要
在线性科学中，具有一般D'Anembert Wave解决方案的波运动方程是基本模型之一。 D'AlemberT波是在固定模型（材料）依赖性速度下沿一个方向移动的任意行进波。但是，当引入非线性效应以进行波动时，遗漏了d'AlemberT波。在本文中，我们研究了特殊（2+1） - 二维的Koteweg-de Vries（KDV）方程，即所谓的Nizhnik-Novikov-Veselov（NNV）方程的可能的行驶波解决方案和孤子分子。从NNV方程式重新发现了错过的D'Alembert Wave。通过使用速度共振机理，发现孤子分子与D'Alembert波密切相关。实际上，NNV方程的孤子分子可以看作是特殊的d'Alembert波。还讨论了特殊的D'Alembt型波（$ n $ - soliton分子和孤子 - 溶解分子）和孤子之间的相互作用解决方案。
In linear science, the wave motion equation with general D'Alembert wave solutions is one of the fundamental models. The D'Alembert wave is an arbitrary travelling wave moving along one direction under a fixed model (material) dependent velocity. However, the D'Alembert waves are missed when nonlinear effects are introduced to wave motions. In this paper, we study the possible travelling wave solutions, multiple soliton solutions and soliton molecules for a special (2+1)-dimensional Koteweg-de Vries (KdV) equation, the so-called Nizhnik-Novikov-Veselov (NNV) equation. The missed D'Alembert wave is re-discovered from the NNV equation. By using the velocity resonance mechanism, the soliton molecules are found to be closely related to D'Alembert waves. In fact, the soliton molecules of the NNV equation can be viewed as special D'Alembert waves. The interaction solutions among special D'Alembert type waves ($n$-soliton molecules and soliton-solitoff molecules) and solitons are also discussed.
