Acta mathematica scientia,Series A ›› 1999, Vol. 19 ›› Issue (4): 373-378.
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(Institute of Mathematics, Fudan Uiversity, 200433)
| |(Institute of Mathematics, Dalian University of Technology, Dalian 116024
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Abstract:
Some new symmetry reductions and similarity solutions of variant Boussinesq equations systems are given by using direct method developed by clarkson and kruskal recently. Duffing equation and painlené Ⅱ type equation are included in reduction equations. Both poles and algebraic branch point for t can be entered into the solutions of variant Boussinesq equations.
Key words: Ｂｏｕｓｓｉｎｅｓｑｅｑｕａｔｉｏｎｓｙｓｔｅｍｓ, Ｄｉｒｅｃｔｍｅｔｈｏｄ, Ｒｅｄｕｃｔｉｏｎ, Ｅｘａｃｔｓｏｌｕｔｉｏｎ．
CLC Number:
Fan Engui Zhang Hongqing. Symmetry reductions and similarity solutions of variant boussintsq equation systems[J].Acta mathematica scientia,Series A, 1999, 19(4): 373-378.
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http://121.43.60.238/sxwlxbA/EN/Y1999/V19/I4/373
１ ＳａｃｈｓＲＬ．ＯｎｔｈｅｉｎｔｅｇｒａｂｌｅｖａｒｉａｎｔｏｆｔｈｅＢｏｕｓｓｉｎｅｓｑｓｙｓｔｅｍ：Ｐａｉｎｌｅｖｅｐｒｏｐｅｒｔｙ，ｒａｔｉｏｎａｌｓｏｌｕｔｉｏｎｓ，ａｒｅｌａｔｅｄｍａｎｙｂｏｄｙｓｙｓｔｅｍａｎｄｅｑｕｉｖａｌｅｎｃｅｗｉｔｈｔｈｅＡＫＮＳｈｉｅｒａｒｃｈｙ．ＰｈｙｓｉｃａＤ，１９８８，３０：１－８ ２ Ｗｈｉｔｈａｍ ＧＢ．Ｌｉｎｅａｒａｎｄｎｏｎｌｉｎｅａｒｗａｖｅｓ．Ｎｅｗ Ｙａｒｋ：Ｗｉｌｅｙ ＆ Ｓｏｎｓ，１９７３，２１－３０９ ３ Ｗａｎｇ Ｍ Ｌ．ＳｏｌｉｔａｒｙｗａｖｅｓｏｌｕｔｉｏｎｓｆｏｒｖａｒｉａｎｔＢｏｓｓｉｎｅｓｑｅｑｕａｔｉｏｎｓ．ＰｈｙｓＬｅｔｔＡ，１９９５，１９９：１６９－１７２ ４ ＣｌａｒｊｓｏｎＰＡ，ＫｒｕｓｋａｌＭ Ｄ．ＮｅｗｓｉｍｉｌａｒｉｔｙｒｅｄｕｃｔｉｏｎｓｏｆｔｈｅＢｏｕｓｓｉｎｅｓｑｅｑｕａｔｉｏｎ．ＪＭａｔｈＰｈｙｓ，１９８９，３０（１０）：２２０１－２２１３ ５ ＣｌａｒｋｓｏｎＰＡ，ＭａｎｓｆｉｅｌｄＥＬ．Ｓｙｍｍｔｒｙｒｅｄｕｃｔｉｏｎｓａｎｄｅｘａｃｔｓｏｌｕｔｉｏｎｓｏｆａｃｌａｓｓｏｆｎｏｎｌｉｎｅａｒｈｅａｔｅｑｕａｔｉｏｎｓ．ＰｈｙｓｉｃａＤ，１９９３，７０：２５０－２８８ ６ ＬｏｕＳＹ．ＳｉｍｉｌｉｒｉｔｙｓｏｌｕｔｉｏｎｓｏｆＫａｄｏｍｔｓｅｖＰｅｔｖｉａｓｈｖｉｌｌｉｅｑｕａｔｉｏｎ．ＪＰｈｙｓＡ，１９９０，２３：Ｌ６４９－Ｌ６５４ ７ ＡｂｌｏｗｉｔｚＭＪ．Ｓｏｌｉｔｏｎｓｎｏｎｌｉｎｅａｒｅｖｏｌｕｔｉｏｎｅｑｕａｔｉｏｎａｎｄｉｎｖｅｒｓｅｓｃａｔｔｅｒｉｎｇ．Ｎｅｗ Ｙｏｒｋ：ＣａｍｂｒｉｄｇｅＵｎｉｖｅｒｓｉｔｙＰｒｅｓｓ，１９９１，３８１－４９５
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