Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation

Adrien Dekkers, Anna Rozanova-Pierrat, Vladimir Khodygo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (SciVal)
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We relate together different models of non linear acoustic in thermo-elastic media as the Kuznetsov equation, the Westervelt equation, the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation and the Nonlinear Progressive wave Equation (NPE) and estimate the time during which the solutions of these models keep closed in the L2 norm. The KZK and NPE equations are considered as paraxial approximations of the Kuznetsov equation. The Westervelt equation is obtained as a nonlinear approximation of the Kuznetsov equation. Aiming to compare the solutions of the exact and approximated systems in found approximation domains the well-posedness results (for the Kuznetsov equation in a half-space with periodic in time initial and boundary data) are obtained.

Original languageEnglish
Pages (from-to)4231-4258
Number of pages28
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue number7
Early online date27 Apr 2020
Publication statusPublished - 01 Jul 2020


  • Approximations
  • Kuznetsov
  • KZK
  • Non-linear acoustic
  • NPE
  • Westervelt equations


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