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

Name: Comparison of nonlocal nonlinear wave equations in the long-wave limit
Author: Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

İsim	Comparison of nonlocal nonlinear wave equations in the long-wave limit
Yazar	Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Basım Tarihi:	2020-11-17
Basım Yeri	- Taylor & Francis
Konu	Approximation, Nonlocal wave equation, Improved Boussinesq equation, Long-wave limit
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	0003-6811
Kayıt Numarası	7c3488d2-ff5c-47f4-a57f-cd0dc98e46df
Lokasyon	Natural and Mathematical Sciences
Tarih	2020-11-17
Örnek Metin	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

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

Yazar Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

Basım Tarihi 2020-11-17

Basım Yeri - Taylor & Francis

Konu Approximation, Nonlocal wave equation, Improved Boussinesq equation, Long-wave limit

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 0003-6811

Kayıt Numarası 7c3488d2-ff5c-47f4-a57f-cd0dc98e46df

Lokasyon Natural and Mathematical Sciences

Tarih 2020-11-17

Örnek Metin 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