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The Darboux Transformation of the (2+1)-dimensional KP Equation and Its Explicit Solutions

Author: WangLiMin
Tutor: LiXueMei
School: Zhengzhou University
Course: Basic mathematics
Keywords: ( L ) - dimensional soliton equations Darboux transformation Exact solution
CLC: O175.29
Type: Master's thesis
Year: 2011
Downloads: 21
Quote: 0
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Abstract


This paper studies the precise dimensional KP equation solving ( 21 ) Darboux transformation method . Article is divided into five parts , the first part is the introduction , introduces the basic theory of the Darboux transformation of the second part from a new 2 × 2 matrix spectral problem obtained a family of nonlinear soliton equations . third part ( 21 ) -dimensional KP equation is decomposed into two ( 11 ) -dimensional soliton equations , and then construct a Darboux transformation . fourth part of the third part compatibility exact solution for a Darboux transformation N times extended to strict proof . fifth part of the trivial solution u = 0 , u = 1 as seed solution , two ( 11 ) -dimensional soliton equations Darboux transformation ( 21 ) then get the exact solution of the dimensional KP equation .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations > Nonlinear partial differential equations
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