Abstract
In this paper, taking the 2+1-dimensional sine-Gordon equation as an example, we present the concatenating method to construct the multisymplectic schemes. The method is to independently discretize the PDEs in different directions with symplectic schemes, so that the multisymplectic schemes can be constructed by concatenating those symplectic schemes. By this method, we can construct multisymplectic schemes, including some widely used schemes with an accuracy of any order. The numerical simulation on the collisions of solitons is proposed to illustrate the efficiency of the multisymplectic schemes.
| Original language | English |
|---|---|
| Pages (from-to) | 18-30 |
| Number of pages | 13 |
| Journal | Science in China, Series A: Mathematics, Physics, Astronomy |
| Volume | 47 |
| Issue number | 1 |
| State | Published - Feb 2004 |
Funding
Acknowledgements This work was supported by the National Natural Science Foundation of China Innovation Group (No. 40221503), the CAS Hundred Talent Project, the National Key Development Planning Project for the Basic Research (No. 1999032081) and the National Natural Science Foundation of China (Grant No. 10226012).
Keywords
- 2+1-dimensional sine-Gordon equation
- Concatenating method
- Multisymplectic scheme
- Solitons
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