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Interaction of Two Pulsatory Waves of the Korteweg-de Vries Equation in a Zigzag Hyperbolic Structure
Department of Mathematics, College of Mount Saint Vincent, New York, USA
- 1 Department of Mathematics, College of Mount Saint Vincent, New York, USA
American Journal of Computational Mathematics·Volume 04 (2014)·Pages 254–270·Published 17 April 2014·DOI10.4236/ajcm.2014.43022
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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.
KeywordsKdV EquationTwo Pulsatory WavesZHT StructureExperimentalTheoretical Computation
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