On SK and KK Integrable Systems
arxiv(2024)
Abstract
To obtain new integrable nonlinear differential equations there are some
well-known methods such as Lax equations with different Lax representations.
There are also some other methods which are based on integrable scalar
nonlinear partial differential equations. We show that some systems of
integrable equations published recently are the M_2-extension of
integrable scalar equations. For illustration we give Korteweg-de Vries,
Kaup-Kupershmidt, and Sawada-Kotera equations as examples. By the use of such
an extension of integrable scalar equations we obtain some new integrable
systems with recursion operators. We give also the soliton solutions of the
system equations and integrable standard nonlocal and shifted nonlocal
reductions of these systems.
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