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Article Contents

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

• * Corresponding author

The second author is supported by TUBITAK Grant 2215 -Graduate Scholarship Programme for International Students

• In this article we are concerned with the existence of traveling wave solutions of a general class of nonlocal wave equations: $~u_{tt}-a^{2}u_{xx}=(β * u^{p})_{xx}$, $~p>1$. Members of the class arise as mathematical models for the propagation of waves in a wide variety of situations. We assume that the kernel $β$ 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.

Mathematics Subject Classification: Primary: 74H20, 74J30; Secondary: 35Q51, 35A15.

 Citation:

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