Author
Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Publication Date
2020-11-17
Publication Place
-
Taylor & Francis
Subject
Approximation, Nonlocal wave equation, Improved Boussinesq equation, Long-wave limit
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
0003-6811
Record ID
7c3488d2-ff5c-47f4-a57f-cd0dc98e46df
Library Location
Natural and Mathematical Sciences
Date
2020-11-17
Sample Text
We consider a general class of convolution-type nonlocal wave equations modeling bidirectional nonlinear wave propagation. The model involves two small positive parameters measuring the relative strengths of the nonlinear and dispersive effects. We take two different kernel functions that have similar dispersive characteristics in the long-wave limit and compare the corresponding solutions of the Cauchy problems with the same initial data. We prove rigorously that the difference between the two solutions remains small over a long time interval in a suitable Sobolev norm. In particular, our results show that, in the long-wave limit, solutions of such nonlocal equations can be well approximated by those of improved Boussinesq-type equations.
DOI
10.1080/00036811.2019.1577393
Cilt
99
