KdV 1-soliton u = 2κ²·sech²(κ(x - 4κ²t)) satisfies u_t+6uu_x+u_xxx=0 exactly

Exact symbolic verification of the canonical Korteweg-de Vries one-soliton. Ansatz u(x, t) = 2κ²·sech²(κ(x - 4κ²·t)); differentiate u_t, u_x, u_xxx and substitute into u_t + 6u·u_x + u_xxx; residual simplifies to 0 identically (sympy…