Abstract
We study the integrability aspects of an N=1 supersymmetric coupled dispersionless (SUSY-CD) integrable system in detail. We present a superfield Lax representation of the SUSY-CD system by writing its (3×3)-matrix superfield Lax pair and show that the zero-curvature condition corresponds to the SUSY-CD system. From the fermionic superfield Lax representation, we obtain a set of coupled superfield Riccati equations that we further use to obtain an infinite set of superfield conserved currents. We investigate the Darboux transformation of the SUSY-CD system and use it to obtain multisoliton solutions of the system.
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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 195, No. 3, pp. 381–390, June, 2018.
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Mirza, A., Hassan, M. Integrability Properties of A Supersymmetric Coupled Dispersionless Integrable System. Theor Math Phys 195, 825–833 (2018). https://doi.org/10.1134/S004057791806003X
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DOI: https://doi.org/10.1134/S004057791806003X