Gauge transformation and symmetries of the commutative multi-component BKP hierarchy

Abstract

In this paper, we defined a new multi-component BKP hierarchy which takes values in a commutative subalgebra of $gl(N,\mathbb{C})$. After this, we give the gauge transformation of this commutative multi-component BKP (CMBKP) hierarchy. Meanwhile we construct a new constrained CMBKP hierarchy which contains some new integrable systems including coupled KdV equations under a certain reduction. After this, the quantum torus symmetry and quantum torus constraint on the tau function of the commutative multi-component BKP hierarchy will be constructed.

15 pages

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Cited by in corpus (1)

• Bäcklund transformations of $Z_n$-Sine-Gordon systems