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New Two-Componet Coupled KdV Equation and its Connection with the Generalized Harry Dym Equation

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 نشر من قبل Ziemowit Popowicz
 تاريخ النشر 2012
  مجال البحث فيزياء
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 تأليف Ziemowit Popowicz




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It is shown that, two different Lax operators in the Dym hierarchy, produce two generalized coupled Harry Dym equations. These equations transform, via the reciprocal link, to the coupled two-component KdV system. The first equation gives us new integrable two-component KdV system while the second reduces to the known symmetrical two-component KdV equation. For this new two-component coupled KdV system the Lax representation and Hamiltonian structure is defined.



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It is shown that, three different Lax operators in the Dym hierarchy, produce three generalized coupled Harry Dym equations. These equations transform, via the reciprocal link, to the coupled two-component KdV system. The first equation gives us know n integrable two-component KdV system while the second reduces to the known symmetrical two-component KdV equation. The last one reduces to the Drienfeld-Sokolov equation. This approach gives us new Lax representation for these equations.
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