Journal of Evolution Equations

, Volume 16, Issue 3, pp 539–567 | Cite as

A new highly nonlinear shallow water wave equation



We derive a quasilinear shallow water equation directly from the governing equations for gravity water waves within a certain regime for large-amplitude waves which has not been studied so far. Furthermore, we demonstrate local well-posedness of the corresponding Cauchy problem and finally discuss some aspects of the blowup behavior of solutions.


Shallow water equation Large-amplitude waves Cubic nonlinearity Well-posedness 

Mathematics Subject Classification

Primary 35Q35 Secondary 35L30 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria

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