On the structure of the two-soliton interaction for the Korteweg-de Vries equation (Q1286361)

The following result is established for the Korteweg-de Vries equation \(u_t-6uu_x+u_{xxx}=0\), in regard to the structure of the two-soliton interaction: For a given fixed pair of positive real numbers \(k_1\) and \(k_2\), the set of all two-soliton solutions with eigenvalues \(k_1\) and \(k_2\) is extendable to a two-dimensional real linear space, isomorphic to \(\mathbb{R}^2\). This isomorphism carries the set of all two-soliton solutions into the first quadrant of \(\mathbb{R}^2\).