Exact Solutions in 1+1 Dimensions of the General Two-Velocity Discrete Illner Model

Lü Xianqing; Mei Shengwei; Li Minshan

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Article Navigation > Applied Mathematics and Mechanics > 1998 > 19(12): 1101-1106

Lü Xianqing, Mei Shengwei, Li Minshan. Exact Solutions in 1+1 Dimensions of the General Two-Velocity Discrete Illner Model[J]. Applied Mathematics and Mechanics, 1998, 19(12): 1101-1106.

Citation:

Lü Xianqing, Mei Shengwei, Li Minshan. Exact Solutions in 1+1 Dimensions of the General Two-Velocity Discrete Illner Model[J]. Applied Mathematics and Mechanics, 1998, 19(12): 1101-1106.

Citation:

Lü Xianqing, Mei Shengwei, Li Minshan. Exact Solutions in 1+1 Dimensions of the General Two-Velocity Discrete Illner Model[J]. Applied Mathematics and Mechanics, 1998, 19(12): 1101-1106.

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Exact Solutions in 1+1 Dimensions of the General Two-Velocity Discrete Illner Model

1.
Department of Applied Mathematics, Qinghua University, Beijing 100084, P. R. China;
2.
Departmet of Electrical Engineering, Qinghua University, Beijing 100084, P. R. China;
3.
Departmet of Mathematics, Northern Jiaotong University, Beijing 100044, P. R. China

Received Date: 1997-03-24
Rev Recd Date: 1998-05-25
Publish Date: 1998-12-15

Abstract

Abstract

The Illner,model is the most general two-velocity model of the discrete Boltoman equation.It includes,as particular cases,both the Carleman and the MeKean model.Exact solutions in 1+1 dunensions of the general two-velocity discrete Illner model can be studied in a concise way.The conclusions of the precursors need anredliorating.A new type of exact solutions in 1+1 dimensions is obtained.This gives a general method for studying non-trivial exact solutions for the similar discrete Boltzmann equation.
- discrete Boltzmann equation,
- Illner model,
- travelling wave solution,
- bisoliton solution

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References(5)

References

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[2]	T.Platkowski and R.Illner,Discrete velocity models of the Boltzmann equation: a survey on the muthematical aspects of the theory,SLAM Review,30,2(1988),213-255.
[3]	Roberto Monaco and Luigi Preziosi,Fluid Dynamic Applications of the Discrete Boltzmann Equation,World Scientific,Singapore(1991),b3-198.
[4]	Henri Cornille,Exact solutions in 1+1 dimensions of the general two-velocity discrete Illner model,J.Math.Phys.,28,7(1987),1567-1579.
[5]	J.Wick,Two classes of explicit solutions of the Carleman model,Math.Methods Appl.Sci.,6(1984),515-519.