Abstract
We construct a nonauto Darboux transformation for the extended noncommutative Kadomtsev–Petviashvili (ncKP) hierarchy and consequently derive its quasi-Wronskian solution. We also obtain the quasi-Wronskian solution of the ncKP equation with self-consistent sources (ncKPESCS) as a by-product. Finally, we use the direct verification method to prove the quasi-Wronskian solution of the ncKPESCS.
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This research is supported by the National Natural Science Foundation of China (Grant Nos. 11201178 and 11271266), the Fujian National Science Foundation (Grant No. 2012J01013), the Beijing National Science Foundation (Grant No. 1162003), the Fujian Higher College Special Project of Scientific Research (Grant No. JK2012025), and the Fujian Provincial Visiting Scholar Program.
Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 192, No. 1, pp. 51–69, July, 2017.
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Wu, H., Liu, J. & Li, C. Quasideterminant solutions of the extended noncommutative Kadomtsev–Petviashvili hierarchy. Theor Math Phys 192, 982–999 (2017). https://doi.org/10.1134/S0040577917070042
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DOI: https://doi.org/10.1134/S0040577917070042