Ground state travelling waves in infinite lattices

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• 作者：Luyu ZHANG ^{zhangluyu2009@163.com" class="auth_mail" title="E-mail the corresponding author} ; Shiwang MA ^{shiwangm@163.net" class="auth_mail" title="E-mail the corresponding author}
• 关键词：FPU lattice ; ground state wave ; Nehari manifold
• 刊名：Acta Mathematica Scientia
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：36
• 期：3
• 页码：782-790
• 全文大小：343 K

文摘

In this paper, we consider FPU lattices with particles of unit mass. The dynamics of the system is described by the infinite system of second order differential equationsthmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S025296021630039X&_mathId=si1.gif&_user=111111111&_pii=S025296021630039X&_rdoc=1&_issn=02529602&md5=5f6e71149ab8f4209f5e01b5acdd9930">gLazyJSB inlineImage" height="27" width="315" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S025296021630039X-si1.gif">t>t="27" border="0" style="vertical-align:bottom" width="315" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S025296021630039X-si1.gif">t>thContainer hidden">thCode">th altimg="si1.gif" overflow="scroll">t="true">q¨n=U'(qn+1−qn)−U'(qn−qn−1),text> text>n∈ℤ,th>where q_n denotes the displacement of the n-th lattice site and U is the potential of interaction between two adjacent particles. Inspired by previous work due to Szulkin and Weth (Ground state solutions for some indefinite variational problems, J. Funct. Anal., 257 (2009), 3802-3822), we investigate the existence of solitary ground waves, i.e., nontrivial solutions with least possible energy.