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Two new multi-component BKP hierarchies. (English) Zbl 1179.37087
The multi-component KP hierarchy contains many physically relevant nonlinear integrable systems, such as Davey-Stewartson equation, two-dimensional Toda lattice and three-wave resonant interaction ones; and attracts a lot of interests from both physical and mathematical points of view. In this work, the authors introduce a new type of Lax equations that consist of the new time. The flow and the evolutions of wave functions, which give rise to the first kind of a new mcBKP hierarchy. The authors use this hierarchy to obtain the first and the second types of BKPSCS (BKP with self-consistent sources) and their related Lax representations. Moreover, this new mcBKP hierarchy can be reduced to two integrable hierarchies. In particular, the two mcBKP hierarchies provide an effective way to find $(1+1)$-dimensional and $(1+2)$-dimensional soliton equations as well as their Lax representations.

MSC:
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
37K40Soliton theory, asymptotic behavior of solutions
35Q51Soliton-like equations
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