一般两速离散Illner模型的1+1维精确解<sup>*</sup>

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一般两速离散Illner模型的1+1维精确解^*

基金项目: 国家自然科学基金资助(19631060)和中国博士后基金

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

摘要: Illner模型是最一般的Boltzmann方程的两速模型,它包括Carleman模型和McKean模型作为两种特殊情形.离散Ilner模型1+1维精确解能够以一种简洁的方式进行研究.前人的结论需要修正.我们得到了一类新的1+1维精确解.这给出了研究类似的离散Boltzmann方程精确行波解的一般方法.
- 离散Boltzmann方程 /
- Illner模型 /
- 行波解 /
- 双孤子解
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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[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.

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