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

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DOI: 10.4236/ajcm.2014.43022    5,175 Downloads   5,997 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Miroshnikov, V. (2014) Interaction of Two Pulsatory Waves of the Korteweg-de Vries Equation in a Zigzag Hyperbolic Structure. American Journal of Computational Mathematics, 4, 254-270. doi: 10.4236/ajcm.2014.43022.

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