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 ) [ PDF ]
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. Liao, S.J.: “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，“超越摄动：同伦分析方法基本思想及其应用”，《力学进展》，２００８年，第３８卷，第１期，１-３４页（中文综述论文）[ PDF ]
16. 廖世俊，“同伦分析方法：求解强非线性问题的一个新途径”，《科学观察》，２００９年，第４卷，第５期，４８-４９页（热点研究论文特约稿）[ PDF ]
17. 廖世俊，“同伦分析方法：研究背景和现状”，《科学观察》，２０１１年，第６卷，第６期，５５-５８页（热点研究论文特约稿）[ 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]
28. Li, X.C., Yu, Z.Y., Liao, S.J.: Observation
of two-dimensional Faraday waves in extremely shallow depth. PHYSICAL REVIEW E, 92:033014
(2015).
[PDF]
[Movie 1][Movie 2][Movie 3]
29. Liao, S.J., Zhao, Y. L.: On the method of directly defining inverse mapping for nonlinear differential equations. Numerical Algorithms, pp.1-32 (2015). [PDF]
30. Qin, S.J., Liao, S. J.: Influence of
numerical noises on computer-generated simulation of spatio-temporal
chaos. Chaos, Solitons & Fractals, 136:109790 (2020). [PDF]
31. Hu, T.L., Liao, S. J.: On the risks of using
double precision in numerical simulations of spatio-temporal
chaos. Journal of Computational Physics, 418:109629 (2020). [PDF]
32. Liao, S. J., Qin, S.J.: Ultra-Chaos: an
insurmountable objective obstacle of reproducibility and replication. Advances
in Applied Mathematics and Mechanics, 14(4):799-815 (2022). [PDF]
33. Qin, S.J., Liao, S. J.: Large-scale influence
of numerical noises as artificial stochastic disturbances on a sustained
turbulence. Journal of Fluid Mechanics, 948:A7
(2022). [PDF]
34. Liao, S. J.: Avoiding small denominator
problems by means of the homotopy analysis method. Advances
in Applied Mathematics and Mechanics, 15(2):267-299 (2023). [PDF]
35. Yang, Y., Qin, S.J., Liao, S. J.: Ultra-chaos
of a mobile robot: a higher disorder than normal-chaos. Chaos, Solitons
& Fractals, 167:113037 (2023). [PDF]
36. Qin, S.J. and Liao, S.J.: A kind of lagrangian
chaotic property of the arnold–beltrami–childress flow. Journal of Fluid Mechanics, 960:A15 (2023).[PDF]
37. Qin, S.J., Yang, Y., Huang, Y.X., Mei, X.Y., Wang, L.P. and Liao, S.J.: Is a
direct numerical simulation (DNS) of navier-stokes equations with small enough grid spacing and time-step definitely reliable/correct?. Journal of Ocean Engineering and Science, 9(3):293–310 (2024).[PDF]
38. Li, J.Y., Liu, Z., Borthwick, A. G. L., Cui, J. and Liao, S.J.: Steady-state
interfacial gravity waves with one-dimensional class-III triad resonance. Physical Review Fluids, 9(9):094801 (2024).[PDF]
39. Qin, S.J. and Liao, S.J.: Influences of artificial
numerical noise on statistics and qualitative properties of chaotic system. Physica D: Nonlinear Phenomena, 470:134355 (2024).[PDF]
40. Liao, S.J. and Qin, S.J.: Physical significance
of artificial numerical noise in direct numerical simulation of turbulence. Journal of Fluid Mechanics, 1008:R2 (2025).[PDF]
41. Liao, S.J. and Qin, S.J.: Noise-expansion
cascade: An origin of randomness of turbulence. Journal of Fluid Mechanics, 1009:A2 (2025).[PDF]
42. Jiang, P., Liao, S.J., Liu, L., Xie, B.: Effects of
appendages on the turbulence and flow noise of a submarine model using high-order scheme. Physics of Fluids, 37(9):095199 (2025).[PDF]
43. Qin, S.J. and Liao, S.J.: Clean
numerical simulation of three-dimensional turbulent kolmogorov flow. Physics of Fluids, 37(10):105160 (2025).[PDF]
44. Liao, S.J.: HAM-schrödingerisation: A generic
framework of quantum simulation for any nonlinear PDEs. Advances in Applied Mathematics and Mechanics, 18(1):1–10 (2025).[PDF]
45. Zhang, B. and Liao, S.J.: An automated
parallel program of clean numerical simulation for chaotic systems governed by ODEs. Computer Physics Communications, 317:109855 (2025).[PDF]
46. Lin, C. and Liao, S.J.: Convergent series of
stokes waves of arbitrary height in deep water via machine learning. Journal of Fluid Mechanics, 1025:A23 (2025).[PDF]
47. Chen, D.Z., Liao, S.J., Xie, B.: An accurate
THINC scheme for interface capturing based on homotopy analysis method. Journal of Computational Physics, 544:114420 (2026).[PDF]
48. Liao, S.J.: Mathematical proof of spatial
symmetry invariance of two-dimensional Kolmogorov flow. Theoretical and Mathematical Physics, 228(2):1304-1314 (2026).[PDF][PDF-Russa]
49. Qin, S.J., Xu, K., Liao, S.J.: Ultra-chaotic property
of Navier–Stokes turbulence. European Journal of Mechanics - B/Fluids, 119:204540 (2026).[PDF]
50. Zhao, D.S., Liao, S.J.: Nonlinear resonance
mechanisms and cross-order harmonic coupling of deep-water waves excited by a moving pressure field. Physics of Fluids, 38(9):092105 (2026).[PDF]
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