Skip to main content

News about Scitation

In December 2016 Scitation will launch with a new design, enhanced navigation and a much improved user experience.

To ensure a smooth transition, from today, we are temporarily stopping new account registration and single article purchases. If you already have an account you can continue to use the site as normal.

For help or more information please visit our FAQs.

banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
/content/aip/journal/adva/5/11/10.1063/1.4936638
1.
1.M. Affouf and R.E. Caflsch, “A numerical study of Riemann problem solutions and stability for a system of viscous conservation laws of mixed type,” SIAM J. Appl. Math. 51, 605-634 (1991).
http://dx.doi.org/10.1137/0151031
2.
2.M. Slemrod and J.E. Flaherty, Numerical integration of a Riemann problem for a van der Waals fluid (Elsevier, Amsterdam, 1986).
3.
3.H. Fan, “A vanishing viscosity approach on the dydamics of phase transitions in Van Der Waals fluids,” J. Differential Equations. 103, 179-204 (1993).
http://dx.doi.org/10.1006/jdeq.1993.1046
4.
4.H. Hattori, “The Riemann problem and the existence of weak solution to a system of Mixed-type in dynamic phase transition,” J. Differential Equations. 146, 287-319 (1998).
http://dx.doi.org/10.1006/jdeq.1998.3433
5.
5.H. Hattori, “The existence and large time behavior of solutions to a system related to a phase transition problem,” SIAM J. Math. Anal. 34(4), 774-804 (2003).
http://dx.doi.org/10.1137/S0036141001391378
6.
6.M. Shearer and Y. Yang, “The Riemann problem for a system of conservation laws of mixed type with a cubic nonlinearity,” P. Roy. Soc. Edinb. A. 125, 675-699 (1995).
http://dx.doi.org/10.1017/S0308210500030298
7.
7.J. Mercier and B. Piccoli, “Admissible Riemann Solvers for Genuinely Nonlinear p-Systems of Mixed Type,” J. Differential Equations. 180, 395-426 (2002).
http://dx.doi.org/10.1006/jdeq.2001.4066
8.
8.D.J. Korteweg, “Sur la forme que prennent lea quation des mouvements des fluids si l’on tient compte des forces capillarires par des variations de densit,” Arch. Neerl. Sci. Exactes Nat. Ser. II. 6, 1-24 (1901).
9.
9.B.U. Felderhof, “The gas-liquid interface near a critical point,” Phys. 48, 541-560 (1970).
10.
10.V. Bongiorno, L.E. Scriven, and H.T. Davis, “Molecular theory of fluid interfaces,” J. Colloid. Interface. Sci. 57, 462-475 (1976).
http://dx.doi.org/10.1016/0021-9797(76)90225-3
11.
11.D.Q. Lu and A.T. Chwang, “Unsteady free-surface waves due to a submerged body moving in a viscous fluid,” Phys. Rev. E. 71, 066303 (2005).
http://dx.doi.org/10.1103/PhysRevE.71.066303
12.
12.V. Bongiorno, L.E. Scriven, and H.T. Davis, “Molecular theory of fluid interfaces,” Int. J. Nonlin. Mech. 72, 80-83 (2015).
http://dx.doi.org/10.1016/j.ijnonlinmec.2015.03.004
13.
13.W.X. Ma and J.H. Lee, “A transformed rational function method and exact solutions to the 3 + 1 dimensional Jimbo-Miwa equation,” Chaos. Solitons. Fract. 42, 1356-1363 (2009).
http://dx.doi.org/10.1016/j.chaos.2009.03.043
14.
14.W.X. Ma, H. Wu, and J. He, “Partial differential equations possessing Frobenius integrable decompositions,” Phys. Lett. A. 364, 29-32 (2007).
http://dx.doi.org/10.1016/j.physleta.2006.11.048
15.
15.W.X. Ma and B. Fuchssteiner, “Explicit and Exact Solutions to a Kolmogorov-Petrovskii-Piskunov Equation,” Int. J. Nonlin. Mech. 31, 329-338 (1996).
http://dx.doi.org/10.1016/0020-7462(95)00064-X
16.
16.M. Grillakis, J. Shatah, and W. Strauss, “Stability theory of solitary waves in the presence of symmetry I,” J. Funct. Anal. 74, 160-197 (1987).
http://dx.doi.org/10.1016/0022-1236(87)90044-9
17.
17.M. Grillakis, J. Shatah, and W. Strauss, “Stability theory of solitary waves in the presence of symmetry II,” J. Funct. Anal. 94, 308-348 (1990).
http://dx.doi.org/10.1016/0022-1236(90)90016-E
18.
18.B. Guo and Y. Wu, “Orbital stability of solitary waves for the nonlinear derivative Schrodinger equation,” J. Differential Equations. 123, 35-55 (1995).
http://dx.doi.org/10.1006/jdeq.1995.1156
19.
19.W. Zhang, Y. Qin, Y. Zhao, and B. Guo, “Orbital stability of solitary waves for Kundu equation,” J. Differential Equations. 247, 1591-1615 (2009).
http://dx.doi.org/10.1016/j.jde.2009.05.008
20.
20.S. Hakkaev and K. Kirchev, “Local well-posedness and orbital stability of solitary wave solutions for a generalized Camassa-Holm Equation,” Commun. Part. Diff. Eq. 30, 761-781 (2005).
http://dx.doi.org/10.1081/PDE-200059284
21.
21.X. Liu, Y. Liu, P. Olver, and C. Qu, “Orbital stability of peakons for a generalization of the modified Camassa-Holm equation,” Nonlinearity. 27, 2297-2319 (2014).
http://dx.doi.org/10.1088/0951-7715/27/9/2297
22.
22.C. Qu, Y. Zhang, X. Liu, and Y. Liu, “Orbital stability of periodic peakons to a generalized -Camassa-Holm equation,” Arch. Rational Mech. Anal. 211, 593-617 (2014).
http://dx.doi.org/10.1007/s00205-013-0672-2
23.
23.V. Nemytskii and V. Stepanov, Qualitative theory of differential equations (Dover Publicaton, Dover, 1989).
24.
24.Z. Zhang, T. Ding, W. Huang, and Z. Dong, Qualitative theory of differential equations, Translations of Mathematical Monographs (American Mathematical Society, Providence, 1992).
25.
25.J. Li and L. Zhang, “Bifurcations of traveling wave solutions in generalized Pochhammer-Chree equation,” Chaos. Solitons. Fract. 14, 581-593 (2002).
http://dx.doi.org/10.1016/S0960-0779(01)00248-X
26.
26.W. Zhang, Q. Chang, and B. Jiang, “Explicit exact solitary-wave solutions for compound KdV-type and compound KdV Burgers-type equations with nonlinear term of any order,” Chaos. Solitons. Fract. 13, 311-319 (2002).
http://dx.doi.org/10.1016/S0960-0779(00)00272-1
27.
27.M.E. Taylor, Partial Differential Equations I: Basic Theory, 2nd ed. (Springer, Beijing, 2014).
28.
28.Q. Ye and Z. Li, Introduction of reaction-diffusion equations (Science Press, Beijing, 1990) (in Chinese).
http://aip.metastore.ingenta.com/content/aip/journal/adva/5/11/10.1063/1.4936638
Loading
/content/aip/journal/adva/5/11/10.1063/1.4936638
Loading

Data & Media loading...

Loading

Article metrics loading...

/content/aip/journal/adva/5/11/10.1063/1.4936638
2015-11-23
2016-12-09

Abstract

In this paper, we discuss the existence of traveling wave solutions for compressible fluid equations by applying the theory and method of planar dynamical system, and obtain explicit expressions for all bounded traveling wave solutions by undetermined coefficient method, including kink and bell profile traveling wave solutions, as well as periodic wave solutions. We prove the kink profile solitary wave solution, both sides of which asymptotic values are not zero, is orbitally stable by the theory of Grillakis-Shatah-Strauss orbital stability.

Loading

Full text loading...

/deliver/fulltext/aip/journal/adva/5/11/1.4936638.html;jsessionid=qjsMTRSEM2piFpnnQ1lne30W.x-aip-live-02?itemId=/content/aip/journal/adva/5/11/10.1063/1.4936638&mimeType=html&fmt=ahah&containerItemId=content/aip/journal/adva
true
true

Access Key

  • FFree Content
  • OAOpen Access Content
  • SSubscribed Content
  • TFree Trial Content
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
/content/realmedia?fmt=ahah&adPositionList=
&advertTargetUrl=//oascentral.aip.org/RealMedia/ads/&sitePageValue=aipadvances.aip.org/5/11/10.1063/1.4936638&pageURL=http://scitation.aip.org/content/aip/journal/adva/5/11/10.1063/1.4936638'
Right1,Right2,Right3,