Geodesic
Bilinear identities for an~extended B-type Kadomtsev--Petviashvili hierarchy
Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 3, pp. 357-370

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We construct bilinear identities for wave functions of an extended B-type Kadomtsev–Petviashvili (BKP) hierarchy containing two types of $(2{+}1)$-dimensional Sawada–Kotera equations with a self-consistent source. Introducing an auxiliary variable corresponding to the extended flow for the BKP hierarchy, we find the $\tau$-function and bilinear identities for this extended BKP hierarchy. The bilinear identities generate all the Hirota bilinear equations for the zero-curvature forms of this extended BKP hierarchy. As examples, we obtain the Hirota bilinear equations for the two types of $(2{+}1)$-dimensional Sawada–Kotera equations in explicit form.
Keywords: BKP hierarchy, self-consistent source, bilinear identity, tau function, Hirota bilinear form. 
@article{TMF_2016_186_3_a0,
     author = {Runliang Lin and Tiancheng Cao and Xiaojun Liu and Yunbo Zeng},
     title = {Bilinear identities for an~extended {B-type} {Kadomtsev--Petviashvili} hierarchy},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {357--370},
     publisher = {mathdoc},
     volume = {186},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_186_3_a0/}
}
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Runliang Lin; Tiancheng Cao; Xiaojun Liu; Yunbo Zeng. Bilinear identities for an~extended B-type Kadomtsev--Petviashvili hierarchy. Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 3, pp. 357-370. http://geodesic.mathdoc.fr/item/TMF_2016_186_3_a0/