Elsevier

Applied Mathematics Letters

Volume 98, December 2019, Pages 157-163
Applied Mathematics Letters

Superposition of the coupled NLS and MKdV systems

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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.

Keywords

Hirota equations
Superposition of integrable equations
Ablowitz–Musslimani reduction
Hirota bilinear method
Soliton solutions

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