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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 16
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Research Article

A comparison of solutions of two convolution-type unidirectional wave equations

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Pages 4422-4431 | Received 05 Feb 2022, Accepted 23 Aug 2022, Published online: 30 Aug 2022

References

  • Erbay HA, Erbay S, Erkip A. A semi-discrete numerical method for convolution type unidirectional wave equations. J Comput Appl Math. 2021;387:112496.
  • Benjamin TB, Bona JL, Mahony JJ. Model equations for long waves in nonlinear dispersive systems. Philos Trans R Soc Lond A: Math Phys Sci. 1972;272:47–78.
  • Rosenau P. Dynamics of dense discrete systems: high order effects. Prog Theor Phys. 1988;79:1028–1042.
  • Erbay HA, Erbay S, Erkip A. Comparison of nonlocal nonlinear wave equations in the long-wave limit. Appl Anal. 2020;99:2670–2679.
  • Bona JL, Colin T, Lannes D. Long wave approximations for water waves. Arch Ration Mech Anal. 2005;178:373–410.
  • Constantin A, Lannes D. The hydrodynamical relevance of the Camassa–Holm and Degasperis–Procesi equations. Arch Ration Mech Anal. 2009;192:165–186.
  • Duchene V, Israwi S, Talhouk R. A new fully justified asymptotic model for the propagation of internal waves in the Camassa-Holm regime. SIAM J Math Anal. 2015;47:240–290.
  • Lannes D. The water waves problem: mathematical analysis and asymptotics. Providence (RI): American Mathematical Society; 2013. (AMS mathematical surveys and monographs; vol. 188).
  • Lannes D, Linares F, Saut JC. The Cauchy problem for the Euler–Poisson system and derivation of the Zakharov–Kuznetsov equation. Prog Nonlinear Differ Equ Appl. 2013;84:181–213.
  • Kato T, Ponce G. Commutator estimates and the Euler and Navier–Stokes equations. Commun Pure Appl Math. 1988;41:891–907.
  • Taylor ME. Partial differential equations II: qualitative studies of linear equations. 2nd ed. New York (NY): Springer; 2011.

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