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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |