Quasi-periodic solutions for perturbed generalized KdV equation

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• 作者：Lufang Mi^a ; ^{milufang@126.com" class="auth_mail" title="E-mail the corresponding author} ; Kangkang Zhang^b ; ^{11110180026@fudan.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Generalized KdV equation ; KAM theory ; Birkhoff normal form ; Quasi-periodic solutions
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：32
• 期：Complete
• 页码：314-337
• 全文大小：789 K

文摘

We consider the generalized KdV equation u_t=−u_xxx+30u⁴u_x$u_t=-u_{xxx}+30u^4{u}_x$ subject to periodic boundary conditions. We prove that the existence of many 2-dimensional invariant tori under sufficiently small Hamiltonian perturbations by means of infinite-dimensional KAM theory and partial Birkhoff normal form and thus many time quasi-periodic solutions for the above perturbed equation.