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Journal of Zhejiang University SCIENCE A 2008 Vol.9 No.10 P.1457-1462


An implicit symmetry constraint of the modified Korteweg-de Vries (mKdV) equation

Author(s):  Ying YOU, Jing YU, Qiao-yun JIANG

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   youying1024@126.com, yujing615@126.com

Key Words:  Implicit symmetry constraint, Completely integrable Hamiltonian system, Modified Korteweg-de Vries (mKdV) equation

Ying YOU, Jing YU, Qiao-yun JIANG. An implicit symmetry constraint of the modified Korteweg-de Vries (mKdV) equation[J]. Journal of Zhejiang University Science A, 2008, 9(10): 1457-1462.

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A1 - Qiao-yun JIANG
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.A0820187

In this paper, an implicit symmetry constraint is calculated and its associated binary nonlinearization of the Lax pairs and the adjoint Lax pairs is carried out for the modified Korteweg-de Vries (mKdV) equation. After introducing two new independent variables, we find that under the implicit symmetry constraint, the spatial part and the temporal part of the mKdV equation are decomposed into two finite-dimensional systems. Furthermore we prove that the obtained finite-dimensional systems are Hamiltonian systems and completely integrable in the Liouville sense.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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