Product Representations of Periodic Waves for the Modified Korteweg-de Vries Family of Evolution Equations
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概要
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Periodic waves for evolution equations of the modified Korteweg-de Vries (niKdV) family are expressed as products of elliptic functions. By employing the Hirota bilinear formulation, periodic waves of the single component niKdV with positive cubic nonlinearity are obtained as rational functions of Jacobi elliptic functions. Coupled mKdV systems with two and three components are treated. Dark or Rink type solitary waves can exist for systems where the equation for each component is in the brightsoliton regime. Finally, a coupled system of (2+1) (2 spatial and 1 temporal) dimensional evolution equations is studied. Periodic waves in terms of products of elliptic functions are also derived. Thevalidity of these new solutions is verified independently by a computer algebra software whenever feasible
- 社団法人日本物理学会の論文
- 2003-02-15
著者
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CHOW Kwok
Department of Mechanical Engineering, University of Hong Kong
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Chow Kwok
Department Of Mechanical Engineering University Of Hong Kong
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Chow Kwok
Department Of Mathematics University Of Arizona
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