Bifurcation Approach to Analysis of Travelling Waves in Nonlocal Hydrodynamic-Type Models
The paper considers the nonlocal hydrodynamic-type systems which are two-dimensional travelling wave systems with a five-parameter group. We apply the method of dynamical systems to investigate the bifurcations of phase portraits depending on the parameters of systems and analyze the dynamical behav...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/893279 |
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| _version_ | 1832559399194853376 |
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| author | Jianping Shi Jibin Li |
| author_facet | Jianping Shi Jibin Li |
| author_sort | Jianping Shi |
| collection | DOAJ |
| description | The paper considers the nonlocal hydrodynamic-type systems which are two-dimensional
travelling wave systems with a five-parameter group. We apply the
method of dynamical systems to investigate the bifurcations of phase portraits depending
on the parameters of systems and analyze the dynamical behavior of the
travelling wave solutions. The existence of peakons, compactons, and periodic cusp
wave solutions is discussed. When the parameter n equals 2, namely, let the isochoric
Gruneisen coefficient equal 1, some exact analytical solutions such as smooth
bright solitary wave solution, smooth and nonsmooth dark solitary wave solution,
and periodic wave solutions, as well as uncountably infinitely many breaking wave
solutions, are obtained. |
| format | Article |
| id | doaj-art-1c8e2df00107498f93dca4b3784e69f6 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1c8e2df00107498f93dca4b3784e69f62025-02-03T01:30:09ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/893279893279Bifurcation Approach to Analysis of Travelling Waves in Nonlocal Hydrodynamic-Type ModelsJianping Shi0Jibin Li1Department of Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, ChinaDepartment of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, ChinaThe paper considers the nonlocal hydrodynamic-type systems which are two-dimensional travelling wave systems with a five-parameter group. We apply the method of dynamical systems to investigate the bifurcations of phase portraits depending on the parameters of systems and analyze the dynamical behavior of the travelling wave solutions. The existence of peakons, compactons, and periodic cusp wave solutions is discussed. When the parameter n equals 2, namely, let the isochoric Gruneisen coefficient equal 1, some exact analytical solutions such as smooth bright solitary wave solution, smooth and nonsmooth dark solitary wave solution, and periodic wave solutions, as well as uncountably infinitely many breaking wave solutions, are obtained.http://dx.doi.org/10.1155/2014/893279 |
| spellingShingle | Jianping Shi Jibin Li Bifurcation Approach to Analysis of Travelling Waves in Nonlocal Hydrodynamic-Type Models Abstract and Applied Analysis |
| title | Bifurcation Approach to Analysis of Travelling Waves in Nonlocal Hydrodynamic-Type Models |
| title_full | Bifurcation Approach to Analysis of Travelling Waves in Nonlocal Hydrodynamic-Type Models |
| title_fullStr | Bifurcation Approach to Analysis of Travelling Waves in Nonlocal Hydrodynamic-Type Models |
| title_full_unstemmed | Bifurcation Approach to Analysis of Travelling Waves in Nonlocal Hydrodynamic-Type Models |
| title_short | Bifurcation Approach to Analysis of Travelling Waves in Nonlocal Hydrodynamic-Type Models |
| title_sort | bifurcation approach to analysis of travelling waves in nonlocal hydrodynamic type models |
| url | http://dx.doi.org/10.1155/2014/893279 |
| work_keys_str_mv | AT jianpingshi bifurcationapproachtoanalysisoftravellingwavesinnonlocalhydrodynamictypemodels AT jibinli bifurcationapproachtoanalysisoftravellingwavesinnonlocalhydrodynamictypemodels |