Thus the solutions ψ ψ ( u ) are just the Legendre functions P λ λ μ μ ( tanh ⁡ ⁡ ( x ) ) with E = − − μ μ 2 2 , and λ λ = 1 , 2 , 3 ⋯ ⋯ , μ μ = 1 , 2 , ⋯ ⋯ , λ λ − − 1 , λ λ . Moreover, eigenvalues and scattering data can be explicitly computed. In the special case of integer λ λ , the potential is reflectionless and such potentials also arise as the N-soliton solutions of the Korteweg–De Vries equation.