The ε correction of one and two solitons solutions for the KdV hierarchy
碩士 === 國立交通大學 === 應用數學系所 === 94 === In this thesis we study Darboux -Backlund transformations (DBTs) for the q-deformed Korteweg -de Vries hierarchy by using the q-deformed pseudodifferential operators. The elementary DBTs are triggered by the gauge operators T constructed from the wave functions of...
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| Format: | Others |
| Language: | en_US |
| Published: |
2006
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| Online Access: | http://ndltd.ncl.edu.tw/handle/36285929176901613724 |
| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 94 === In this thesis we study Darboux -Backlund transformations (DBTs) for the q-deformed Korteweg -de Vries hierarchy by using the q-deformed pseudodifferential operators.
The elementary DBTs are triggered by the gauge operators T constructed from the wave functions of the associated linear systems. In order to obtain the new solution from
the old one , we have to choose certain gauge operator. Iterating these elementary DBTs, we obtain one and two solitons solutions. In addition we also figure out the correction of one and two solitons for the KdV hierarchy by letting ε equal to q − 1 and q approach 1(which will
recovers q-KdV to the ordinary KdV).
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