Periodic traveling wave solution for non-homogeneous BBM and KdVB equations

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• 作者：Marcos A. de Farias ^{marcosfarias@dm.ufscar.br" class="auth_mail" title="E-mail the corresponding author} ; Cezar I. Kondo ^{dcik@dm.ufscar.br" class="auth_mail" title="E-mail the corresponding author} ; José ; R. dos Santos Filho ; ^{santos@dm.ufscar.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Traveling wave ; Periodic solution ; BBM equation ; KdVB equation
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：34
• 期：Complete
• 页码：563-573
• 全文大小：600 K

文摘

In this paper the Green’s function method and results about fixed point are used to get existence results on periodic traveling wave solution for non-homogeneous problems of generalized versions of the BBM and KdVB equations. It is shown through the constructions of explicit Green’s functions that the periodic boundary value problems for the traveling wave solutions of the BBM and KdVB equations are equivalent to integral equations which generate compact operators in the space of periodic functions. These integral representations allowed us to prove that if the speed of the wave propagation is suitably chosen, then the BBM and KdVB equations will admit periodic traveling wave solution.