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Differential Equations

, Volume 54, Issue 9, pp 1137–1146 | Cite as

Exact Solutions of a Second-Order Nonlinear Partial Differential Equation

  • A. I. Aristov
Partial Differential Equations
  • 21 Downloads

Abstract

The equation ∂2u/∂tx + upu/∂x = uq describing a nonstationary process in semiconductors, with parameters p and q that are a nonnegative integer and a positive integer, respectively, and satisfy p + q ≥ 2, is considered in the half-plane (x, t) ∈ ℝ × (0,∞). All in all, fourteen families of its exact solutions are constructed for various parameter values, and qualitative properties of these solutions are noted. One of these families is defined for all parameter values indicated above.

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References

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    Korpusov, M.O. and Lukyanenko, D.V., Instantaneous blow-up versus local solvability for one problem of propagation of nonlinear waves in semiconductors, J. Math. Anal. Appl., 2018, vol. 459, pp. 159–181.MathSciNetCrossRefzbMATHGoogle Scholar
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    Kudryashov, N.A., Metody nelineinoi matematicheskoi fiziki (Methods of Nonlinear Mathematical Physics), Dolgoprudnyi: Intellekt, 2010.Google Scholar
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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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