Superposition of the coupled NLS and MKdV systems
Date
2019
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Source Title
Applied Mathematics Letters
Print ISSN
0893-9659
Electronic ISSN
Publisher
Elsevier
Volume
98
Issue
Pages
157 - 163
Language
English
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Abstract
Superpositions of hierarchies of integrable equations are also integrable. The superposed equations, such as the Hirota equations in the AKNS hierarchy, cannot be considered as new integrable equations. Furthermore if one applies the Hirota bilinear method to these equations one obtains the same N-soliton solutions of the generating equation which differ only by the dispersion relations. Similar discussions can be made for the locally and nonlocally reduced equations as well. We give, as an example, AKNS system of equations in (1 + 1)-dimensions.