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Volume 12, Issue 1
On the Periodic Solutions of the Davey-Stewartson Systems

Gino Biondini & Dmitri Kireyev

DOI: 10.4208/eajam.310321.230821

East Asian J. Appl. Math., 12 (2022), pp. 1-21.

Published online: 2021-10

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  • Abstract

The periodic, traveling wave solutions of all four versions of the Davey-Stewartson system (namely the focusing and the defocusing cases of both the Davey-Stewartson I and the Davey-Stewartson II equations) are derived and classified. For all four versions, these solutions are described in terms of elliptic functions. Special reductions and limiting cases, including harmonic limits, soliton limits, and one-dimensional solutions, are also explicitly discussed.

  • Keywords

Davey-Stewartson, periodic solutions, solitons, elliptic functions.

  • AMS Subject Headings

35Q51, 35B10, 35C08, 37K10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-12-1, author = {Biondini , Gino and Kireyev , Dmitri}, title = {On the Periodic Solutions of the Davey-Stewartson Systems}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {12}, number = {1}, pages = {1--21}, abstract = {

The periodic, traveling wave solutions of all four versions of the Davey-Stewartson system (namely the focusing and the defocusing cases of both the Davey-Stewartson I and the Davey-Stewartson II equations) are derived and classified. For all four versions, these solutions are described in terms of elliptic functions. Special reductions and limiting cases, including harmonic limits, soliton limits, and one-dimensional solutions, are also explicitly discussed.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.310321.230821}, url = {http://global-sci.org/intro/article_detail/eajam/19917.html} }
TY - JOUR T1 - On the Periodic Solutions of the Davey-Stewartson Systems AU - Biondini , Gino AU - Kireyev , Dmitri JO - East Asian Journal on Applied Mathematics VL - 1 SP - 1 EP - 21 PY - 2021 DA - 2021/10 SN - 12 DO - http://doi.org/10.4208/eajam.310321.230821 UR - https://global-sci.org/intro/article_detail/eajam/19917.html KW - Davey-Stewartson, periodic solutions, solitons, elliptic functions. AB -

The periodic, traveling wave solutions of all four versions of the Davey-Stewartson system (namely the focusing and the defocusing cases of both the Davey-Stewartson I and the Davey-Stewartson II equations) are derived and classified. For all four versions, these solutions are described in terms of elliptic functions. Special reductions and limiting cases, including harmonic limits, soliton limits, and one-dimensional solutions, are also explicitly discussed.

Biondini , Gino and Kireyev , Dmitri. (2021). On the Periodic Solutions of the Davey-Stewartson Systems. East Asian Journal on Applied Mathematics. 12 (1). 1-21. doi:10.4208/eajam.310321.230821
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