Completeness of the exact-solution families for local and nonlocal Fokas–Lennels equations

Determine whether the reported exact hyperbolic, trigonometric, periodic, and algebraic solution families exhaust all possible solutions of the local Fokas–Lennels equation and the integrable nonlocal Fokas–Lennels equation, and identify additional solutions if they do not.

Background

The paper derives numerous exact solutions of the integrable local Fokas–Lennels equation, including solutions with nonzero and zero integration constants, and shows that many of them also solve the integrable nonlocal Fokas–Lennels equation. Despite this extensive catalogue, the authors explicitly state that it is not evident whether all possible solutions have been found.

The unresolved issue concerns the completeness of the solution families for both nonlinear equations and the possibility of discovering further exact solutions beyond those presented in the paper.