Blow-up solutions to the Korteweg–de Vries equation

We deal with singular solutions to the Korteweg–de Vries equation which blow up at finite time. We examine solutions both for initial-boundary value problems and for the Cauchy problem.
We give an estimate of blow-up time depending on the boundary and initial conditions.
In conclusion, we demonstrate the explicit form of the blow-up solution of the Cauchy problem and show the mechanism of the blow-up of this solution.