Complex and singular solutions of KdV and MKdV equations
The Korteweg-de Vries (KdV) and the modified Korteweg-de Vries (MKdV) equations are shown to have, besides the regular real solutions, exact regular complex as well as singular solutions. The singular solution for the KdV is real but for the MKdV it is pure imaginary. Implications of the complex solutions are discussed.
Buti, B.↗