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Miura Transformation Between The Partial Differential Equation

Posted on:2006-12-22Degree:MasterType:Thesis
Country:ChinaCandidate:C Y XuFull Text:PDF
GTID:2190360152492594Subject:Basic mathematics
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In this paper, we study Miura transformations uâ†'v from partial differential equations u_xxx = F{u,u_x,u_t) to nonlinear partial differential equationsdefined using integrable systems on v. We classify allsuch Miura transformations under some restrictions, and hence generalize the classical Miura transformations to a large class of nonlinear partial differential equations. For some examples, by applying Miura transformations found in this paper, we derive exact solutions v from known solutions u. In particular, kink and soliton -kink solutions ofare obtained from constant solutions and soliton solutions of the MKdV equation. As another application of Miura transformations of this paper, we deduce a new Backhund transformation for each of andfrom the known Backhand transformation for the MKdV equation.
Keywords/Search Tags:Miura transformations, integrable systems, Backlund transformations
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