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On the Behavior of Solutions of a Class of Nonlinear Partial Differential Equations

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Abstract

The behavior of the steady-state (or the traveling wave) solutions for a class of nonlinear partial differential equations is studied. The nonlinearity in these equations is expressed by the presence of the convective term. It is shown that the steady-state (or the traveling wave) solution may explode at a finite value of the spatial (or the characteristic) variable. This holds whatever the order of the spatial derivative term in these equations. Furthermore, new special solutions of a set of equations in this class are also found.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Cairo University, Cairo, Egypt

    H. I. Abdel-Gawad

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  1. H. I. Abdel-Gawad
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Abdel-Gawad, H.I. On the Behavior of Solutions of a Class of Nonlinear Partial Differential Equations. Journal of Statistical Physics 97, 395–407 (1999). https://doi.org/10.1023/A:1004683522126

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  • DOI: https://doi.org/10.1023/A:1004683522126

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