@Article{AAMM-4-5,
author = {Xiang, Li and Zhang, Weiguo and Zhao, Yan},
title = {Shape Analysis and Solution to a Class of Nonlinear Wave Equation with Cubic Term},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2012},
volume = {4},
number = {5},
pages = {559--574},
abstract = {<p style="text-align: justify;">In this paper, we analyze the relation between the shape of the 
bounded traveling wave solutions and dissipation coefficient of
nonlinear wave equation with cubic term by the theory and method of
planar dynamical systems. Two critical values which can characterize
the scale of dissipation effect are obtained. If dissipation effect
is not less than a certain critical value, the traveling wave
solutions appear as kink profile; while if it is less than this
critical value, they appear as damped oscillatory. All expressions
of bounded traveling wave solutions are presented, including exact
expressions of bell and kink profile solitary wave solutions, as
well as approximate expressions of damped oscillatory solutions. For
approximate damped oscillatory solution, using homogenization
principle, we give its error estimate by establishing the integral
equation which reflects the relations between the exact and
approximate solutions. It can be seen that the error is an
infinitesimal decreasing in the exponential form.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.10-m11181},
url = {https://global-sci.com/article/73559/shape-analysis-and-solution-to-a-class-of-nonlinear-wave-equation-with-cubic-term}
}