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New Expressions of Periodic Waves and a Novel Phenomenon in a Compressible Hyperelastic Rod
| Content Provider | Semantic Scholar |
|---|---|
| Author | Zheng-Rong Zhang Bengong |
| Copyright Year | 2007 |
| Abstract | A In this paper, we employ both bifurcation method of dynamical sys- tems and numerical exploration of difierential equations to investigate the periodic waves of a general compressible hyperelastic rod equation ut + 3uux i uxxt i ∞(2uxuxx + uuxxx) = 0; with parameter ∞ < 0. New expressions including explicit expressions and implicit expressions are obtained. Some previous results are extended. Specially, a new phe- nomenon is found: when the initial value tends to a certain number, the periodic shock wave suddenly changes into a smooth periodic wave. In dynamical systems, this repre- sents that one of orbits can pass through the singular line. The coherency of numerical simulation and theoretical derivation implies the correctness of our results. |
| Starting Page | 80 |
| Ending Page | 96 |
| Page Count | 17 |
| File Format | PDF HTM / HTML |
| Volume Number | 20 |
| Alternate Webpage(s) | https://admin.global-sci.org/uploads/Issue/JPDE/v20n1/201-7_short.pdf |
| Alternate Webpage(s) | http://www.global-sci.org/v1/jpde/issue/v20/n1/pdf/201-7.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
