On some canonical classes of cubic-quintic nonlinear Schrödinger equations

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• 作者：C. &Ouml ; zemir <sup>ozemir@itu.edu.tr" class="auth_mail" title="E-mail the corresponding authorsup>
• 关键词：Nonlinear Schr&ouml ; dinger ; Lie symmetry ; Blow-up
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：446
• 期：2
• 页码：1814-1832
• 全文大小：440 K

文摘

In this paper we bring into attention variable coefficient cubic&ndash;quintic nonlinear Schr&ouml;dinger equations which admit Lie symmetry algebras of dimension four. Within this family, we obtain the reductions of canonical equations of nonequivalent classes to ordinary differential equations using tools of Lie theory. Painlevé integrability of these reduced equations is investigated. Exact solutions through truncated Painlevé expansions are achieved in some cases. One of these solutions, a conformal-group invariant one, exhibits blow-up behavior in finite time in <span id="mmlsi1" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X1630542X&_mathId=si1.gif&_user=111111111&_pii=S0022247X1630542X&_rdoc=1&_issn=0022247X&md5=9eeb950a94df5882532c221ae7c5847f" title="Click to view the MathML source">L<sub>psub>span><span class="mathContainer hidden"><span class="mathCode">scroll">sub>Lpsub>span>span>span>, <span id="mmlsi2" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X1630542X&_mathId=si2.gif&_user=111111111&_pii=S0022247X1630542X&_rdoc=1&_issn=0022247X&md5=f3da1373d63c1d263a6815a6ac5d282f" title="Click to view the MathML source">L<sub>∞sub>span><span class="mathContainer hidden"><span class="mathCode">scroll">sub>L∞sub>span>span>span> norm and in distributional sense.