The q-deformed mKP hierarchy with self-consistent sources, Wronskian solutions and solitons
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2010
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IOP Publishing Ltd
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Abstract
Based on the eigenfunction symmetry constraint of the q-deformed modified KP hierarchy, a q-deformed mKP hierarchy with self-consistent sources (q-mKPHSCSs) is constructed. The q-mKPHSCSs contain two types of q-deformed mKP equation with self-consistent sources. By the combination of the dressing method and the method of variation of constants, a generalized dressing approach is proposed to solve the q-deformed KP hierarchy with self-consistent sources (q-KPHSCSs). Using the gauge transformation between the q-KPHSCSs and the q-mKPHSCSs, the q-deformed Wronskian solutions for the q-KPHSCSs and the q-mKPHSCSs are obtained. The one-soliton solutions for the q-deformed KP (mKP) equation with a source are given explicitly.
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©IOP Publishing Ltd.
The authors are grateful to the referees for the quite valuable comments. This work is supported by National Basic Research Program of China (973 Program) 2007CB814800) and National Natural Science Foundation of China (grand No. 10801083 and 10901090). RL acknowledges the economical support from “Banco
Santander–Tsinghua University” program for his stay in UCM, and he also thanks the Departamento de Física Te´orica II (UCM) for the warm hospitality.