论文标题
Fokas-Lenells方程的可集成还原和孤子
Integrable reduction and solitons of the Fokas-Lenells equation
论文作者
论文摘要
新型的孤子结构是为Fokas-Lenells方程式构建的。在这样做的过程中，在讨论了连续波的稳定性之后，使用多个尺度扰动理论将方程式减少到Korteweg-de Vries系统，该系统的相对孤子解决方案可以提高原始系统的复杂（且相当意外）的解决方案。都考虑了聚焦和散热方程式，并且发现在两种情况下都可能存在黑暗孤子，而在聚焦的情况下，也有可能。这些发现令人惊讶，因为相对非线性schrödinger方程没有表现出这些解决方案。
Novel soliton structures are constructed for the Fokas-Lenells equation. In so doing, and after discussing the stability of continuous waves, a multiple scales perturbation theory is used to reduce the equation to a Korteweg-de Vries system whose relative soliton solution gives rise to intricate (and rather unexpected) solutions to the original system. Both the focusing and defocusing equations are considered and it is found that dark solitons may exist in both cases while in the focusing case antidark solitons are also possible. These findings are quite surprising as the relative nonlinear Schrödinger equation does not exhibit these solutions.
