Comparison of nonlocal nonlinear wave equations in the long-wave limit

Erbay, H. A. and Erbay, S. and Erkip, Albert (2020) Comparison of nonlocal nonlinear wave equations in the long-wave limit. Applicable Analysis, 99 (15). pp. 2670-2679. ISSN 0003-6811 (Print) 1563-504X (Online)

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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.
Item Type: Article
Uncontrolled Keywords: 35C20; 35Q53; 35Q74; 74J30; Adrian Constantin; Approximation; improved Boussinesq equation; long-wave limit; nonlocal wave equation
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Albert Erkip
Date Deposited: 31 Jul 2023 12:55
Last Modified: 31 Jul 2023 12:56

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