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Similarity solutions of the generalized Kadomtsev-Petviashvili-Burgers equations

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Il Nuovo Cimento B (1971-1996)

Summary

Group analysis allows us to find similarity solutions for the equation\(\left( {u_t + \frac{J}{{2t}}u + J_1 uu_x + J_2 u_{xx} + J_3 u_{xxx} } \right)_x + J_1 (t)u_{yy} = 0\) This equation defines the effects of nonlinearity, dispersion and dissipation in many problems of bidimensional propagation in a continuous medium. Some features of these invariant solutions are also examined.

Riassunto

Con i metodi dell'analisi gruppale si determinano le soluzioni di similarità dell'equazione\(\left( {u_t + \frac{J}{{2t}}u + J_1 uu_x + J_2 u_{xx} + J_3 u_{xxx} } \right)_x + J_1 (t)u_{yy} = 0\) Questa equazione regge gli effetti di non linearità, di dispersione e dissipazione in problemi di propagazione ondosa bidimensionale in mezzi continui. Si esaminano, inoltre, aleune caratteristiche di queste soluzioni invarianti.

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Authors and Affiliations

  1. Istituto di Aeronautica della Facoltà di Ingegneria dell'Università, Palermo

    P. Barrera

  2. Istituto Matematico della Facoltà di Ingegneria dell'Università, Palermo

    T. Brugarino

Authors
  1. P. Barrera
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  2. T. Brugarino
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To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.

This work was supported by CNR-GNFM and MPI of Italy.

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Barrera, P., Brugarino, T. Similarity solutions of the generalized Kadomtsev-Petviashvili-Burgers equations. Nuov Cim B 92, 142–156 (1986). https://doi.org/10.1007/BF02732643

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  • DOI: https://doi.org/10.1007/BF02732643

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