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

has been cited by the following article:

• TITLE: Interaction of Two Pulsatory Waves of the Korteweg-de Vries Equation in a Zigzag Hyperbolic Structure

  AUTHORS: Victor A. Miroshnikov

  KEYWORDS: KdV Equation, Two Pulsatory Waves, ZHT Structure, Experimental, Theoretical Computation

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.4 No.3, June 24, 2014

  ABSTRACT: 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.