A New Example of Explode-Decay Solitary Waves in One-Dimension

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  • Nakamura Akira
    Physics Laboratory, Osaka University of Foreign Studies
  • Hirota Ryogo
    Department of Applied Mathematics, Faculty of Engineering, Hiroshima University

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  • A New Example of Explode Decay Solitary

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We have found a new example of the 1+1 dimensional explode-decay solitary waves. The equation is the classical Boussinesq equation written as ut=((1+u)v−vxx)x, vt=(u+(1⁄2)v2)x where subscripts represent partial derivatives. The explode-decay solitary wave solutions are expressed by the Hermite polynomials. Bäcklund transform and the inverse scattering transform scheme have been obtained. We have shown that the present solutions are related to the rational solutions of the nonlinear Schrödinger equation iψt+ψxx−2ψ*ψψ=0.

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