  Multisoliton solutions of the KdV equation satisfy nonlinear ordinary
differential equations which are known as stationary equations for the KdV
hierarchy, or sometimes as Lax-Novikov equations. An interesting feature of
these equations, known since the 1970's, is that they can be explicitly
integrated, by virtue of being finite-dimensional completely integrable
Hamiltonian systems. Here we use the integration theory to investigate the
question of whether the multisoliton solutions are the only nonsingular
solutions of these ordinary differential equations which vanish at infinity. In
particular we prove that this is indeed the case for $2$-soliton solutions of
the fourth-order stationary equation.
