Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 346, Issue 1, Pages 255-261Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2008.05.055
Keywords
Fornberg-Whitham equation; traveling wave solution; bifurcation method
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In this paper, by using bifurcation method, we successfully find the Fornberg-Whitham equation u(t) - u(xxt) + u(x) = uu(xxx) - uu(x) + 3u(x)u(xx). has a type of traveling wave solutions called kink-like wave solutions and antikink-like wave solutions. They are defined on some semifinal bounded domains and possess properties of kink waves and anti-kink waves. Their implicit expressions are obtained. For some concrete data, the graphs of the implicit functions are displayed, and the numerical simulation is made. The results show that Our theoretical analysis agrees with the numerical Simulation. Crown Copyright (c) 2008 Published by Elsevier Inc. All rights reserved.
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