A single soliton satisfies only one conservation law, the rest follow. An N-soliton solution satisfies N independent conservation laws, the rest follow. Consider a vector ODE d/dt (x) = A x, A is a matrix, x is a vector. Let A = BDB^{-1}, where D is in Jordan canonical form Then the solution of the ODE is x =B ext (At) B^{-1} x_0. The conserved quantities are the eigenvalues of A. It is somewhat similar with KdV and other integrable systems.

Dear @ Mikhail Kovalyov ,

Thanks a lot for nice reply. Please send some relevant reference books, papers, or links.

Best wishes and regards.