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.