发表机构
LyRIDS, ECE Engineering School, OMNES Education（OMNES教育旗下ECE工程师学院LyRIDS）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推广Hirota三孤子判据至超对称情形，证明超对称双线性KdV型方程存在三超孤子解需满足八个可积性条件，并据此完成此类方程的分类，揭示Hietarinta分类在超对称框架下的有效子集。
AI 中文摘要
我们提出了允许无约束三超孤子解的超对称双线性KdV型方程的分类。将Hirota经典三孤子判据推广到超对称情形，我们推导出控制三超孤子解存在的完整玻色子和费米子相容性条件。我们证明了每个超对称双线性KdV型方程都具有无约束的单超孤子和双超孤子解，而三超孤子解仅在满足八个可积性条件时才存在。这些条件提供了Hirota经典可积性判据的超对称类比，并自然地恢复了Carstea先前引入的费米子关系，揭示了其结构起源。作为结果，我们对Hirota双线性KdV型方程的超对称扩展进行了分类，并表明在无约束超对称框架下，Hietarinta经典分类中仅有一子集仍然有效。
英文摘要
We present a classification of supersymmetric bilinear KdV-type equations admitting unconstrained three-super-soliton solutions. Extending Hirota's classical three-soliton criterion to the supersymmetric setting, we derive the complete bosonic and fermionic compatibility conditions governing the existence of three-super-soliton solutions. We prove that every supersymmetric bilinear KdV-type equation possesses unconstrained one- and two-super-soliton solutions, whereas three-super-soliton solutions exist only when eight integrability conditions are satisfied. These conditions provide a supersymmetric analogue of Hirota's classical integrability criterion and naturally recover the fermionic relations previously introduced by Carstea, revealing their structural origin. As a consequence, we classify the supersymmetric extensions of Hirota bilinear KdV-type equations and show that only a subset of Hietarinta's classical classification remains valid in the unrestricted supersymmetric framework.
Comments23 pages, 1 figure
