Restricted K- and τ-symmetries on multisoliton manifolds of the potential BKP and CKP equations
Abstract
We investigate the reduction of generalized K-symmetries and τ-symmetries on the multisoliton manifolds of the potential BKP and CKP hierarchies. The n-soliton solution of BKP depends on wave-number parameters km, transverse parameters lm, and phase parameters ξm0, defining a 3n-dimensional manifold. Its restricted K-symmetries project onto an n-dimensional phase-shift subspace, while the restricted τ-symmetries engage the full 3n-dimensional tangent space. This structure naturally yields a row-replacement determinant representation. In contrast, the n-soliton solution of CKP has no independent transverse parameters, reducing the manifold dimension to 2n. The restricted K-symmetries again form an n-dimensional phase-shift representation, but the τ-symmetries now involve only 2n tangent directions. For CKP, the natural formulation treats elementary tangent symmetries as unknowns, producing a column-replacement determinant representation via Cramer's rule. The difference between these two determinant structures reflects not a difference in the underlying linear algebra, but rather the distinct parameterizations of the two soliton manifolds. Both formulas express explicitly how infinite-dimensional symmetry hierarchies collapse onto finite-dimensional multisoliton families.
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BibTeX
@misc{hao2026restricted,
title = {{Restricted $K$- and $τ$-symmetries on multisoliton manifolds of the potential BKP and CKP equations}},
author = {Xiazhi Hao and Mingxia Ji and Senyue Lou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34960},
eprint = {2610.34960},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34960},
}
RIS
TY - UNPB
TI - Restricted K- and τ-symmetries on multisoliton manifolds of the potential BKP and CKP equations
AU - Xiazhi Hao
AU - Mingxia Ji
AU - Senyue Lou
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.34960
UR - https://arxiv.org/abs/2610.34960
AB - We investigate the reduction of generalized K-symmetries and τ-symmetries on the multisoliton manifolds of the potential BKP and CKP hierarchies. The n-soliton solution of BKP depends on wave-number parameters k_m, transverse parameters l_m, and phase parameters ξ_m0, defining a 3n-dimensional manifold. Its restricted K-symmetries project onto an n-dimensional phase-shift subspace, while the restricted τ-symmetries engage the full 3n-dimensional tangent space. This structure naturally yields a row-replacement determinant representation. In contrast, the n-soliton solution of CKP has no independent transverse parameters, reducing the manifold dimension to 2n. The restricted K-symmetries again form an n-dimensional phase-shift representation, but the τ-symmetries now involve only 2n tangent directions. For CKP, the natural formulation treats elementary tangent symmetries as unknowns, producing a column-replacement determinant representation via Cramer's rule. The difference between these two determinant structures reflects not a difference in the underlying linear algebra, but rather the distinct parameterizations of the two soliton manifolds. Both formulas express explicitly how infinite-dimensional symmetry hierarchies collapse onto finite-dimensional multisoliton families.
ER -