A new exact solution for nonlinear interaction of two pulsatory waves of the Korteweg-de Vries (KdV) equation is computed by decomposition in an invariant zigzag hyperbolic tangent (ZHT) structure. A computational algorithm is developed by experimental programming with lists of equations and expressions. The structural solution is proved by theoretical programming with symbolic general terms. Convergence, tolerance, and summation of the ZHT structural approximation are discussed. When a reference level vanishes, the two-wave solution is reduced to the two-soliton solution of the KdV equation.
 Zabusky, N.J. and Kruskal, M.D. (1965) Interaction of “Solitons” in a Collisionless Plasma and the Recurrence of Initial States. Physical Review Letters, 15, 240-243. http://dx.doi.org/10.1103/PhysRevLett.15.240
 Hirota, R. (1971) Exact Solutions of the Korteweg-de Vries Equation for Multiple Solitons. Physical Review Letters, 27, 1192-1194. http://dx.doi.org/10.1103/PhysRevLett.27.1192
 Izrar, B., Lusseyran, F. and Miroshnikov, V. (1995) Two-Level Solitary Waves as Generalized Solutions of the KdV Equation. Physics of Fluids, 7, 1056-1062. http://dx.doi.org/10.1063/1.868548
 Varley, E. and Seymour, B.R. (1998) A Simple Derivation of the N-Soliton Solutions to the Korteweg-de Vries Equation. SIAM Journal on Applied Mathematics, 58, 904-911. http://dx.doi.org/10.1137/S0036139996303270
 Miroshnikov, V.A. (2002) The Boussinesq-Rayleigh Approximation for Rotational Solitary Waves on Shallow Water with Uniform Vorticity. Journal of Fluid Mechanics, 456, 1-32. http://dx.doi.org/10.1017/S0022112001007352
 Laitone, E.V. (1960) The Second Approximation to Cnoidal and Solitary Waves. Journal of Fluid Mechanics, 9, 430-444. http://dx.doi.org/10.1017/S0022112060001201
 Grimshaw, R. (1971) The Solitary Wave in Water of Variable Depth. Part 2. Journal of Fluid Mechanics, 46, 611-622.
 Longuet-Higgins, M.S. and Fenton, J.D. (1974) On the Mass, Momentum, Energy, and Circulation of a Solitary Wave II. Proceedings of the Royal Society A, 340, 471-493. http://dx.doi.org/10.1098/rspa.1974.0166
 Pennell, S.A. and Su, C.H. (1984) A Seventeenth-Order Series Expansion for the Solitary Wave. Journal of Fluid Mechanics, 149, 431-443. http://dx.doi.org/10.1017/S0022112084002731
 Pennell, S.A. (1987) On a Series Expansion for the Solitary Wave. Journal of Fluid Mechanics, 179, 557-561.