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TMF, 1994, Volume 99, Number 2, Pages 226–233 (Mi tmf1581)  

Exact solutions to the partially integrable Eckhaus equation

R. Contea, M. Musetteb

a CEA, Service de Physique Théorique
b Vrije Universiteit

Abstract: A partially integrable extension of the Eckhaus equation is first converted to one real fourth order equation. The only integrable case is isolated by simply solving a diophantine equation, and its linearizing transformation, not obvious at first glance, is shown to be the singular part transformation of Painlevé analysis. In the partially integrable case, three exact solutions are found by the truncation procedure. The third one is a six-parameter solution, whose dependence on $x$ is elliptic and dependence on $t$ involves the equation of Chazy.

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English version:
Theoretical and Mathematical Physics, 1994, 99:2, 543–548

Bibliographic databases:

Language: English

Citation: R. Conte, M. Musette, “Exact solutions to the partially integrable Eckhaus equation”, TMF, 99:2 (1994), 226–233; Theoret. and Math. Phys., 99:2 (1994), 543–548

Citation in format AMSBIB
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\by R.~Conte, M.~Musette
\paper Exact solutions to the partially integrable Eckhaus equation
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\yr 1994
\vol 99
\issue 2
\pages 226--233
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\transl
\jour Theoret. and Math. Phys.
\yr 1994
\vol 99
\issue 2
\pages 543--548
\crossref{https://doi.org/10.1007/BF01016136}
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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