79 citations · 1k across the 43 of their papers we have counts for
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A commend on "Three Classes of Newtonian Three-Body Planar Periodic Orbits" by Šuvakov and Dmitrašinović (PRL, 2013)
Xiaoming Li, Shijun Liao
Currently, the fifteen new periodic solutions of Newtonian three-body problem with equal mass were reported by Šuvakov and Dmitrašinović (PRL, 2013) [1]. However, using a reliable…
On cusped solitary waves in finite water depth
Shijun Liao
It is well-known that the Camassa-Holm (CH) equation admits both of the peaked and cusped solitary waves in shallow water. However, it was an open question whether or not the exact…
Physical limit of prediction for chaotic motion of three-body problem
Shijun Liao
A half century ago, Lorenz found the "butterfly effect" of chaotic dynamic systems and made his famous claim that long-term prediction of chaos is impossible. However, the meaning…
On the mathematically reliable long-term simulation of chaos of Lorenz equation in the interval [0,10000]
Shijun Liao, Pengfei Wang
Using 1200 CPUs of the National Supercomputer TH-A1 and a parallel integral algorithm based on the 3500th-order Taylor expansion and the 4180-digit multiple precision data, we have…
Chaotic motion of three-body problem : an origin of macroscopic randomness of the universe
Shijun Liao
The famous three-body problem is investigated by means of a numerical approach with negligible numerical noises in a long enough time interval, namely the Clean Numerical Simulatio…
Two new standing solitary waves in shallow water
Shijun Liao
In this paper, the closed-form analytic solutions of two new Faraday's standing solitary waves due to the parametric resonance of liquid in a vessel vibrating vertically with a con…