A Classification of Hirota-Integrable Supersymmetric Bilinear KdV-Type Equations
Abstract
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.
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BibTeX
@misc{delisle2026classification,
title = {{A Classification of Hirota-Integrable Supersymmetric Bilinear KdV-Type Equations}},
author = {Laurent Delisle and Amine Jaouadi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14372},
eprint = {2609.14372},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14372},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Classification of Hirota-Integrable Supersymmetric Bilinear KdV-Type Equations
AU - Laurent Delisle
AU - Amine Jaouadi
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14372
UR - https://arxiv.org/abs/2609.14372
AB - 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.
ER -