Integrals of motion of the Korteweg–de Vries equation in a class of steplike solutions - Andreiev, K. M. (Reports of the National Academy of Sciences of Ukraine, 2016)
We study the Cauchy problem for the Korteweg–de Vries with steplike initial data. The regilarized integrals of motion are constructed and expressed via associated scattering data of the Schrödinger equation.