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An involutive system and integrable C. Neumann system associated with the modified Korteweg–de Vries hierarchy (1994)

Qiao, Zhijun

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 35 (1994), S. 2978-2982

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: In this article, a system of finite-dimensional involutive functions is presented and proven to be integrable in the Liouville sense. By using the nonlinearization method, the C. Neumann system associated with the modified Korteweg–de Vries (mKdV) hierarchy is obtained. Thus, the C. Neumann system is shown to be completely integrable via a gauge transformation between it and an integrable Hamiltonian system. Finally, the solution of a stationary mKdV equation and the involutive solutions of the mKdV hierarchy are secured. As two examples, the involutive solutions are given for the mKdV equation: vt+1/4vxxx−3/2v2vx=0 and the 5th mKdV equation vt−1/16vxxxxx+5/8v2vxxx +5/2vvxvxx +5/8v3x−3/40v4vx=0.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.530497

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