A numerical study of compactons.

*(English)*Zbl 0932.65096Summary: The Korteweg-de Vries equation has been generalized by P. Rosenau and J. M. Hyman [Compactons: Solitons with finite wavelength, Phys. Rev. Lett. 70, No. 5, 564 (1993)] to a class of partial differential equations that has soliton solutions with compact support (compactons). Compactons are solitary waves with the remarkable soliton property that after colliding with other compactons, they re-emerge with the same coherent shape [loc. cit.]. In this paper, finite difference and finite element methods have been developed to study these types of equations. The analytical solutions and conserved quantities are used to assess the accuracy of these methods. A single compacton as well as the interaction of compactons have been studied. The numerical results have shown that these compactons exhibit true soliton behavior.

##### MSC:

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

35Q51 | Soliton equations |

35Q53 | KdV equations (Korteweg-de Vries equations) |

35Q55 | NLS equations (nonlinear Schrödinger equations) |

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

##### Keywords:

nonlinear Schrödinger equation; Korteweg-de Vries equation; soliton solutions; solitary waves; finite difference; finite element; numerical results
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\textit{M. S. Ismail} and \textit{T. R. Taha}, Math. Comput. Simul. 47, No. 6, 519--530 (1998; Zbl 0932.65096)

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##### References:

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