C-Integrability Test for Discrete Equations via Multiple Scale Expansions
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
C-Integrability Test for Discrete Equations via Multiple Scale Expansions
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| Creator |
Scimiterna, C.
Levi, D. |
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| Description |
In this paper, we are extending the well-known integrability theorems obtained by multiple scale techniques to the case of linearizable difference equations. As an example, we apply the theory to the case of a differential-difference dispersive equation of the Burgers hierarchy which via a discrete Hopf-Cole transformation reduces to a linear differential-difference equation. In this case, the equation satisfies the A₁, A₂ and A₃ linearizability conditions. We then consider its discretization. To get a dispersive equation we substitute the time derivative by its symmetric discretization. When we apply to this nonlinear partial difference equation the multiple scale expansion we find out that the lowest order non-secularity condition is given by a non-integrable nonlinear Schrödinger equation. Thus showing that this discretized Burgers equation is neither linearizable not integrable.
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| Date |
2019-02-09T19:34:04Z
2019-02-09T19:34:04Z 2010 |
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| Type |
Article
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| Identifier |
C-Integrability Test for Discrete Equations via Multiple Scale Expansions / C. Scimiterna, D. Levi // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 27 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 34K99; 34E13; 37K10; 37J30 DOI:10.3842/SIGMA.2010.070 http://dspace.nbuv.gov.ua/handle/123456789/146506 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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