A variational characterization of 2-soliton profiles for the KdV equation

It is well known that 2-soliton profiles for the KdV equation are local minimizers of a constrained variational problem involving three polynomial conservation laws. Here we show that 2-soliton profiles are the global minimizers for this variational problem. The proof, which proceeds via a profile decomposition, also shows that every minimizing sequence converges strongly to the set of minimizing profiles.

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