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topological solitons

Chinese translation: 拓扑孤子

15:52 Feb 7, 2011
English to Chinese translations [PRO]
Science - Mathematics & Statistics
English term or phrase: topological solitons
"a topological soliton or a topological defect is a solution of a system of partial differential equations or of a quantum field theory homotopically distinct from the vacuum solution; it can be proven to exist because the boundary conditions entail the existence of homotopically distinct solutions. Typically, this occurs because the boundary on which the boundary conditions are specified has a non-trivial homotopy group which is preserved in differential equations; the solutions to the differential equations are then topologically distinct, and are classified by their homotopy class. Topological defects are not only stable against small perturbations, but cannot decay or be undone or be de-tangled, precisely because there is no continuous transformation that will map them (homotopically) to a uniform or "trivial" solution."

From wikipedia:http://en.wikipedia.org/wiki/Topological_soliton
Zoe778
Chinese translation:拓扑孤子
Explanation:
在场论中，孤子按照形成的“机理”有拓扑性孤子和非拓扑性孤子之分。
理想的平面波是在空间中无限延伸的，而一般地，由不同频率成分的平面波叠加而成的波包，由于色散而在空间中逐渐弥散，因此也不能完全在空间中局域。如果由于某种原因使得色散效应被抵消，从而波包形状被保持下来，此时便形成了一个孤子。在某些介质中就存在抵消色散效应的非线性效应，从而能形成非拓扑性孤子，例如水波孤子和光学孤子等。另外一种情形是，由于拓扑效应使得波包不会扩撒，从而形成拓扑性孤子，例如扭结。但两种都涉及非线性。




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Note added at 1 day20 hrs (2011-02-09 12:25:59 GMT) Post-grading
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Also, I'd like to take this opportunity to extend my sincere gratitude to the colleagues including pkchan, Guo Feng, Sharon Toh and SophieT, for their kind and professtional help in building this term.
Selected response from:

James_xia
China
Grading comment
4 KudoZ points were awarded for this answer



Summary of answers provided
4 +4拓扑孤子
James_xia


  

Answers


10 mins   confidence: Answerer confidence 4/5Answerer confidence 4/5 peer agreement (net): +4
拓扑孤子


Explanation:
在场论中，孤子按照形成的“机理”有拓扑性孤子和非拓扑性孤子之分。
理想的平面波是在空间中无限延伸的，而一般地，由不同频率成分的平面波叠加而成的波包，由于色散而在空间中逐渐弥散，因此也不能完全在空间中局域。如果由于某种原因使得色散效应被抵消，从而波包形状被保持下来，此时便形成了一个孤子。在某些介质中就存在抵消色散效应的非线性效应，从而能形成非拓扑性孤子，例如水波孤子和光学孤子等。另外一种情形是，由于拓扑效应使得波包不会扩撒，从而形成拓扑性孤子，例如扭结。但两种都涉及非线性。




--------------------------------------------------
Note added at 1 day20 hrs (2011-02-09 12:25:59 GMT) Post-grading
--------------------------------------------------

Also, I'd like to take this opportunity to extend my sincere gratitude to the colleagues including pkchan, Guo Feng, Sharon Toh and SophieT, for their kind and professtional help in building this term.


    Reference: http://www.changhai.org/bbs/load_article.php?fid=3&aid=11005...
James_xia
China
Native speaker of: Chinese
PRO pts in category: 4

Peer comments on this answer (and responses from the answerer)
agree  pkchan
1 hr
agree  Guo Feng
9 hrs
agree  Sharon Toh, MITI MCIL
10 hrs
agree  SophieT
1 day 5 hrs
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