The KP-I equation has family of solutions which decayto zero at space infinity. One of these solutions is theclassical lump solution, which is a traveling wave, andthe KP-I equation in this case reduces to the Boussinesqequation. In this paper we classify all the ‘lump-type’solutions of the Boussinesq equation. Using a robustinverse scattering transform developed by Bilman–Miller for the Schrödinger equation, we show that thelump-type solutions are rational and their 𝜏 functionshave to be polynomials of degree 𝑘(𝑘 + 1) for some inte-ger 𝑘. In particular, this implies that the lump solution isthe unique ground state of the KP-I equation (as conjec-tured by Klein–Saut). The problem studied in this paperwas mentioned in Airault–McKean–Moser, our resultcan be regarded as a two-dimensional analogy of theirtheorem on the classification of rational solutions for theKdV equation.