Vandermonde-like determinants’ representations of Darboux transformations and explicit solutions for the modified Kadomtsev-Petviashvili equation |
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Authors: | Ding-jiang Huang Hong-qing Zhang |
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Institution: | a Department of Mathematics, East China University of Science and Technology, Shanghai 200237, PR China b Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, PR China |
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Abstract: | Recently, the (2+1)-dimensional modified Kadomtsev-Petviashvili (mKP) equation was decomposed into two known (1+1)-dimensional soliton equations by Dai and Geng H.H. Dai, X.G. Geng, J. Math. Phys. 41 (2000) 7501]. In the present paper, a systematic and simple method is proposed for constructing three kinds of explicit N-fold Darboux transformations and their Vandermonde-like determinants’ representations of the two known (1+1)-dimensional soliton equations based on their Lax pairs. As an application of the Darboux transformations, three explicit multi-soliton solutions of the two (1+1)-dimensional soliton equations are obtained; in particular six new explicit soliton solutions of the (2+1)-dimensional mKP equation are presented by using the decomposition. The explicit formulas of all the soliton solutions are also expressed by Vandermonde-like determinants which are remarkably compact and transparent. |
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Keywords: | _method=retrieve& _eid=1-s2 0-S0378437108002975& _mathId=si25 gif& _pii=S0378437108002975& _issn=03784371& _acct=C000053510& _version=1& _userid=1524097& md5=32cbd160789d8457fc937d20bb8e7c1a')" style="cursor:pointer N-fold Darboux transformations" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">N-fold Darboux transformations Explicit solutions Vandermonde-like determinants Soliton equation mKP equation |
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