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періодичних видань НАН України
Symmetries of the Hirota Difference Equation
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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Symmetries of the Hirota Difference Equation
Інший ID:
2010 Mathematics Subject Classification: 35Q51; 37K10; 37K15; 37K40; 39A14
DOI:10.3842/SIGMA.2017.053
DOI:10.3842/SIGMA.2017.053
Посилання:
Symmetries of the Hirota Difference Equation / A.K. Pogrebkov // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 19 назв. — англ.
Підтримка:
This work has been funded by the Russian Academic Excellence Project ‘5-100’.
Дата:
2017
Переглядів:
491
Завантажень:
283
Анотація:
Continuous symmetries of the Hirota difference equation, commuting with shifts of independent variables, are derived by means of the dressing procedure. Action of these symmetries on the dependent variables of the equation is presented. Commutativity of these symmetries enables interpretation of their parameters as ''times'' of the nonlinear integrable partial differential-difference and differential equations. Examples of equations resulting in such procedure and their Lax pairs are given. Besides these, ordinary, symmetries the additional ones are introduced and their action on the Scattering data is presented.
