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Darboux Transformations for (2+1)-Dimensional Extensions of the KP Hierarchy
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Darboux Transformations for (2+1)-Dimensional Extensions of the KP Hierarchy
Інший ID:
2010 Mathematics Subject Classification: 35Q51; 35Q53; 35Q55; 37K35
DOI:10.3842/SIGMA.2015.028
DOI:10.3842/SIGMA.2015.028
Посилання:
Darboux Transformations for (2+1)-Dimensional Extensions of the KP Hierarchy / O. Chvartatskyi, Y. Sydorenko // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 85 назв. — англ.
Підтримка:
The authors are grateful to Professors Folkert M¨uller-Hoissen and Maxim Pavlov for fruitful
discussions and useful advice in preparation of this paper. The authors also wish to express
their gratitude to the referees for their valuable comments and suggestions. O. Chvartatskyi has
been supported via the Alexander von Humboldt foundation. Yu.M. Sydorenko is grateful to
the Ministry of Education, Science, Youth and Sports of Ukraine for partial financial support
(Research Grant MA-107F).
Дата:
2015
Переглядів:
722
Завантажень:
291
Анотація:
New extensions of the KP and modified KP hierarchies with self-consistent sources are proposed. The latter provide new generalizations of (2+1)-dimensional integrable equations, including the DS-III equation and the N-wave problem. Furthermore, we recover a system that contains two types of the KP equation with self-consistent sources as special cases. Darboux and binary Darboux transformations are applied to generate solutions of the proposed hierarchies.
