In this letter, we investigate multisoliton solutions with even numbers and its generated solutions for nonlocal Fokas–Lenells equation over a nonzero background. First, we obtain 2n-soliton solutions with a nonzero background via n-fold Darboux transformation, and find that these soliton solutions will appear in pairs. Particularly, 2n-soliton solutions consist of n ‘bright’ solitons and n ‘dark’ solitons. This phenomenon implies a new form of integrability: even integrability. Then interactions between solitons with even numbers and breathers are studied in detail. To our best knowledge, a novel nonlinear superposition between a kink and 2n-soliton is also generated for the first time. Finally, interactions between some different smooth positons with a nonzero background are derived.

在这封信中，我们研究了具有偶数的多孤子解及其在非零背景下针对非局部Fokas-Lenells方程生成的解。首先，我们通过n倍Darboux变换获得了背景为非零的2个n孤子解，发现这些孤子解将成对出现。特别是，2个n孤子解由n个“亮”孤子和n个“暗”孤子组成。这种现象暗示了一种新的可集成性形式：甚至可集成性。然后详细研究了偶数个孤子与呼吸之间的相互作用。据我们所知，扭结与2 n之间存在新颖的非线性叠加-soliton也是第一次生成。最后，得出具有非零背景的一些不同光滑正电子之间的相互作用。