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Existence of traveling waves for a class of nonlocal nonlinear equations with bell shaped kernels

Erkip, Albert and Ramadan, Abba Ibrahim (2017) Existence of traveling waves for a class of nonlocal nonlinear equations with bell shaped kernels. Communications on Pure and Applied Analysis, 16 (6). 2125 -2132. ISSN 1534-0392 (Print) 1553-5258 (Online) Published Online First http://dx.doi.org/10.3934/cpaa.2017105

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Abstract

In this article we are concerned with the existence of traveling wave solutions of a general class of nonlocal wave equations: utt - a^2uxx = (beta* u^p)xx, p > 1. Members of the class arise as mathematical models for the propagation of waves in a wide variety of situations. We assume that the kernel beta is a bell-shaped function satisfying some mild differentiability and growth conditions. Taking advantage of growth properties of bell-shaped functions, we give a simple proof for the existence of bell-shaped traveling wave solutions.
Item Type: Article
Uncontrolled Keywords: Solitary waves, bell-shaped functions, nonlocal wave equations, variational methods
Subjects: Q Science > QA Mathematics > QA299.6-433 Analysis
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Albert Erkip
Date Deposited: 19 Aug 2017 12:34
Last Modified: 07 Jan 2019 11:07
URI: https://research.sabanciuniv.edu/id/eprint/32955

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