Kadomtsev-Petviashvili type equation for entire range of relative water depths

Serdar Beji*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


A Kadomtsev-Petviashvili type equation valid for the entire range of relative water depths; namely, shallow, intermediate, and deep, is derived. The new equation is capable of simulating the shallow water cnoidal waves and the deep water second-order Stokes waves equally well besides accounting for wave shoaling due to varying water depths. Linear shoaling properties of the equation for unidirectional sinusoidal waves are in complete agreement with the energy flux concept. A finite-difference scheme is adopted for numerical solution of the equation to demonstrate its performance against test cases and its wide range of possible applications.

Original languageEnglish
Pages (from-to)60-68
Number of pages9
JournalCoastal Engineering Journal
Issue number1
Publication statusPublished - 2018

Bibliographical note

Publisher Copyright:
© 2018 Japan Society of Civil Engineers.


  • Arbitrary relative depths
  • Cnoidal waves and Stokes waves
  • Kadomtsev-Petviashvili type equation
  • Varying bathymetry


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