Integrable System: A system of differential equations that admits exact solutions through systematic methods, typically characterised by infinitely many conservation laws and symmetries.

[1] Positive solutions of partial discrete Kirchhoff type problems. Alexandria Engineering Journal (2024). [2] Infinitely Many Solutions for a Boundary Value Problem with Discontinuous Nonlinearities.

The problem has eluded all attempts to find a solution so far. A major milestone was reached in 2005 when Goldston and two colleagues showed that there is an infinite number of prime pairs that ...