Ph.D. Dissertation

 

Liao, S.J.: Proposed homotopy analysis techniques for the solution of nonlinear problems. Ph.D. dissertation, Shanghai Jiaotong University, 1992.

 

Books

 

Liao, S.J.: Beyond Perturbation – Introduction to the Homotopy Analysis Method. Chapman & Hall/CRC, Boca Raton, 2003. ( Booking )

 

Liao, S.J.: Homotopy Analysis Method in Nonlinear Differential Equations. Springer & Higher Education Press, Heidelberg, 2012. ( Booking )

 

Liao, S.J., (ed.): Advances in Homotopy Analysis Method. World Scientific Press, 2013. ( Booking ) [Chapter 1]

 

 

Selected Journal Articles

 

1.     Liao, S.J.: An approximate solution technique which does not depend upon small parameters: a special example.  Int. J. Non-Linear Mechanics, 30: 371-380 (1995).  [ PDF ]

2.     Liao, S.J.: An approximate solution technique which does not depend upon small parameters (Part 2): an application in fluid mechanics. Int. J. Non-Linear Mechanics, 32: 815-822 (1997).  [ PDF ]

3.     Liao, S.J.: An explicit, totally analytic approximation of Blasius’ viscous flow problems.  Int. J. Non-Linear Mechanics, 34(4): 759-778 (1999).  [ PDF ]

4.     Liao, S.J.: A uniformly valid analytic solution of 2D viscous flow past a semi-infinite flat plate. J. Fluid Mechanics, 385: 101-128 (1999).  [ PDF ]

5.     Liao, S.J. and Campo, A.: Analytic solutions of the temperature distribution in Blasius viscous flow problems. J. Fluid Mechanics, 453: 411-425 (2002).  [ PDF ]

6.     Liao, S.J.: On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet. J. Fluid Mechanics, 488: 189-212 (2003).  [ PDF ]

7.     Liao, S.J.: On the homotopy analysis method for nonlinear problems. Applied Mathematics and Computation, 147: 499-513 (2004). [ PDF ]

8.     Liao, S.J.: A new branch of solutions of boundary-layer flows over an impermeable stretched plate. Int. J. Heat and Mass Transfer, 48: 2529-2539 (2005). [ PDF

9.     Liao, S.J.: Series solutions of unsteady boundary-layer flows over a stretching flat plate. Studies in Applied Mathematics, 117: 239-263 (2006). [ PDF ]  

10.  Liao, S.J. and Tan, Y.: A general approach to obtain series solutions of nonlinear differential equations. Studies in Applied Mathematics, 119: 297-354 (2007). [ PDF ]

11.  S.J. Liao, “Notes on the homotopy analysis method: some definitions and theorems”, Communications in Nonlinear Science and Numerical Simulation, vol. 14, pp. 983-997, 2009. [ PDF ]

12.  Xu, H., Lin, Z.L., Liao, S.J., Wu, J.Z. and Majdalani, J.: Homotopy-based solutions of the Navier–Stokes equations for a porous channel with orthogonally moving walls. Physics of Fluids, 22(5): 053601 (2010). [ PDF ]

13.  Li, Y.J., Nohara, B.T. and Liao, S.J.: Series solutions of coupled Van der Pol equation by means of homotopy analysis method. J. Mathematical Physics, 51: 063517 (2010). [ PDF ]

14.  Liao, S.J.: An optimal homotopy-analysis approach for strongly nonlinear differential equations. Communications in Nonlinear Science and Numerical Simulation, 15:2003-2016 (2010). [ PDF ]

15. 廖世俊,“超越动:同分析方法基本思想及其用”,《力学展》,2008年,第38卷,第1期,1-34页(中文文)[ PDF ]

16. 廖世俊,“同分析方法:求解强非线问题的一个新途径”,《科学察》,2009年,第4卷,第5期,48-49页(点研究文特稿)[ PDF ]

17. 廖世俊,“同分析方法:研究背景和状”,《科学察》,2011年,第6卷,第6期,55-58页(点研究文特稿)[ PDF ]

18.  Liao, S.J.: On the reliability of computed chaotic solutions of non-linear differential equations. Tellus, 61(A): 550-564 (2009). [ PDF ] (arXiv:0901.2986)

19.  Liao, S.J.: Chaos – A bridge from micro-level uncertainty to macroscopic randomness.  Communications in Nonlinear Science and Numerical Simulation.  17: 2564-2569 (2012) [PDF] (arXiv:1108.4472). 

20. Liao, S.J.: On the numerical simulation of propagation of micro-level inherent uncertainty for chaotic dynamic systems. Chaos, Solitons & Fractals, 47: 1-12 (2013). [PDF]

21. Xu, D.L., Lin, Z.L., Liao, S.J. and Stiassnie, M.: On the steady-state fully resonant progressive waves in water of finite depth, Journal of Fluid Mechanics, 710:379-418 (2012). [ PDF ]

22. Liao, S.J.: Physical limit of prediction for chaotic motion of three-body problem, Communications in Nonlinear Science and Numerical Simulation, 19:601-616 (2013). [PDF]

23. Liao, S.J.: “Do peaked solitary water waves indeed exist?”, Communications in Nonlinear Science and Numerical Simulation, 19:1792-1821 (2014). [PDF]  [Elsevier AudioSlides]

24. Liao, S.J, Wang, P. F.: On the mathematically reliable long-term simulation of chaotic solutions of Lorenz equation in the interval [0, 10000], SCIENCE CHINA Physics, Mechanics & Astronomy, 57:330-335 (2014). [PDF]

25. Liu, Z. and Liao, S.J.: Steady-state resonance of multiple wave interactions in deep water, Journal of Fluid Mechanics, 742:664-700 (2014). [ PDF ]

26. Li, X.C., Xu, D.L., Liao, S.J.: Observations of highly localized oscillons with multiple crests and troughs, PHYSICAL REVIEW E, 90: 031001(R) (2014). [ PDF ] [Movie 1][Movie 2]

27. Liu, Z., Xu, D. L., Li, J., Peng T., Alsaedi, A., Liao, S. J.: On the existence of steady-state resonant waves in experiments , Journal of Fluid Mechanics, 763:1-23 (2015). [ PDF ]