Acta mathematica scientia,Series A ›› 1999, Vol. 19 ›› Issue (3): 286-292.
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Abstract:
The homogeneous balance method is very effective to seek for solitary wave solution of nonliear evolution equations. in this paper we will give three kinds of important applictions of homogenceous balance method;1)to find new exact solutions for nonlinear evolution equaton;2)to seek for Backlund transformation and Lax parirs of nonlinear evolution ;3)to give symmetry reduction and similarity solution of nonlinear evolution equation .
Key words: Ｈｏｍｏｇｅｎｅｏｕｓｂａｌａｎｃｅ ｍｅｔｈｏｄ, Ｅｘａｃｔｓｏｌｕｔｉｏｎ, Ｂ¨ａｃｋｌｕｎｄｔｒａｎｓｆｏｒｍａｔｉｏｎ, Ｓｉｍｉｌａｒｉｔｙｓｏｌｕｔｉｏｎ．
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Fan Engui Zhang Hongqing. Some New Applications of Homogeneous Balance Method[J].Acta mathematica scientia,Series A, 1999, 19(3): 286-292.
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http://121.43.60.238/sxwlxbA/EN/Y1999/V19/I3/286
１ Ｗａｎｇ Ｍ Ｌ．ＳｏｌｉｔａｒｙｗａｖｅｓｏｌｕｔｉｏｎｆｏｒｖａｒｉａｎｔＢｏｕｓｓｉｎｅｑｅｑｕａｔｉｏｎｓ．ＰｈｙｓＬｅｔｔＡ，１９９５，１９９：１６９－１７２ ２ Ｗａｎｇ Ｍ Ｌ．ＥｘａｃｔｓｏｌｕｔｉｏｎｓｆｏｒａｃｏｍｐｏｕｎｄＫｄＶＢｕｒｇｅｒｓｅｑｕａｔｉｏｎ．ＰｈｙｓＬｅｔｔＡ，１９９６，２１３：２７９－２８７ ３ Ｗａｎｇ Ｍ Ｌ，ｅｃｔ．Ａｐｐｌｉｃａｔｉｏｎｏｆｈｏｍｏｇｅｎｅｏｕｓｂａｌａｎｃｅ ｍｅｔｈｏｄｔｏｅｘａｃｔｓｏｌｕｔｉｏｎｓｏｆｎｏｎｌｉｎｅａｒｅｖｏｌｕｔｉｏｎｅｑｕａｔｉｏｎｉｎｍａｔｈｅｍａｔｉｃａｌｐｈｙｓｉｃｓ．ＰｈｙｓＬｅｔｔＡ，１９９６，２１６：６７－７３ ４ ＴｉａｎＢ，ｅｔｃ．Ｎｅｗｆａｍｉｌｉｅｓｏｆｅｘａｃｔｓｏｌｕｔｉｏｎｓｔｏｔｈｅｉｎｔｅｇｒａｂｌｅｄｉｓｐｅｒｓｉｖｅｌｏｎｇｗａｖｅｅｑｕａｉｔｏｎｓｉｎ （２＋１）ｄｉｍｅｎｓｉｏｎａｌｓｐａｃｅ．ＪＰｈｙｓＡ：ＭａｔｈＧｅｎ，１９９６，２９：２８９５－２９０３ ５ 范恩贵等．非线性波动方程的孤波解．物理学报，１９９７，４６（７）：１２５４－１２５８ ６ ＭａｆｌｉｅｔＷ．Ｓｏｌｉｔａｒｙｗａｖｅｓｏｌｕｔｉｏｎｓｏｆｎｏｎｌｉｎｅａｒｗａｖｅｅｑｕａｔｉｏｎ．ＡｍＪＰｈｙｓ，１９９２，６０（７）：６５０－６５４ ７ 谷超豪等．孤立子理论与应用．浙江科技出版社，１９９０ ８ ＧｕＣ Ｈ．ＯｎｔｈｅＤａｒｂｏｕｘｍａｔｒｉｃｅｓｏｆＢａｃｋｌｕｎｄｔｒａｎｓｆｏｍａｔｉｏｎｓｆｏｒｔｈｅＡＫＮＳｓｙｓｔｅｍ．ＬｅｔｔＭａｔｈＰｈｙｓ，１９８７，１２：１７９ ９ ＮｅｕｇｅｂａｕｅｒＧ，ｅｔｃ．ＧｅｎｅｒａｌＮｓｏｌｉｔｏｎｓｏｌｕｔｉｏｎｏｆｔｈｅＡＫＮＳｃｌａｓｓｏｎａｒｂｉｔｒａｒｙｂａｃｋｇｒｏｕｎｄ．ＰｈｙｓＬｅｔｔＡ，１９８４，１００：４６７－４７０ １０ ＷｅｉｓｓＪ，ｅｔｃ．ＴｈｅＰａｉｎｌｅｖｅｐｒｏｐｅｒｔｙｆｏｒｐａｒｔｉａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ．ＪＭａｔｈＰｈｙｓ，１９８３，２４（３）：５２２－５２６ １１ ＷｅｉｓｓＪ．ＯｎｃｌａｓｓｅｓｏｆｉｎｔｅｇｒａｂｌｅｓｙｓｔｅｍｓａｎｄｔｈｅＰａｉｎｌｅｖｅｐｒｏｐｅｒｔｙ．ＪＭａｔｈＰｈｙｓ，１９８４，２５（１）：１３－２４ １２ ＢｌｕｍａｎＧ Ｗ，ｅｔｃ．Ｕｓｅｏｆｇｒｏｕｐａｎａｌｙｓｉｓｉｎｓｏｌｖｉｎｇｏｖｅｒｄｅｔｅｒｍｉｎｅｄｓｙｓｔｅｍｓｏｆｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ．ＪＭａｔｈＡｎａｌＡｐｐｌ，１９８９，１３８：９５－１０５ １３ ＢｌｕｍａｎＧ Ｗ．Ｓｙｍｍｅｔｒｉｅｓａｎｄｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ．Ｎｅｗ Ｙｏｒｋ：ＳｐｒｉｎｇｅｒＶｅｒｌａｇ，１９８９ １４ ＢｌｕｍａｎＧ Ｗ，ｅｔｃ．Ｎｅｗｓｙｍｍｅｔｒｉｅｓｆｏｒｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ．ＩＭＡＪＡｐｐｌＭａｔｈ，１９８８，４０：８７－９４ １５ ＯｌｖｅｒＰＪ．ＡｐｐｌｉｃａｔｉｏｎｓｏｆＬｉｅｇｒｏｕｐｓｔｏｄｉｆｆｅｒｅｕｔｉａｌｅｑｕａｔｉｏｎｓ．Ｎｅｗ Ｙｏｒｋ：ＳｐｒｉｎｇｅｒＶｅｒｌａｇ，１９８６ １６ ＣｌａｒｋｓｏｎＰＡ．ｅｔｃ．ＮｅｗｓｉｍｉｌａｒｉｔｙｒｅｄｕｃｔｉｏｎｓｏｆｔｈｅＢｏｕｓｓｉｎｅｓｑｅｑｕａｔｉｏｎ．ＪＭａｔｈＰｈｙｓ，１９８９，３０（１０）：２２０１－２２１３ １７ ＣｌａｒｋｓｏｎＰＡ，ｅｔｃ．ＳｙｍｍｅｔｒｙｒｅｄｕｃｔｉｏｎｓｏｆａｇｅｎｅｒａｌｉｚｅｄｃｙｌｉｎｄｒｉｃａｌｎｏｎｌｉｎｅａｒＳｃｈｒｏｄｉｎｇｅｒｅｑｕａｔｉｏｎ．ＪＰｈｙｓＡ：Ｍａｔｈ Ｇｅｎ，１９９３，２６：１３３－１５０ １８ ＬｏｕＳＬ．Ｎｏｎｃｌａｓｓｉｃａｌｓｙｍｍｅｔｒｙｒｅｄｕｃｔｉｏｎｓｆｏｒｔｈｅｄｉｓｐｅｒｓｉｖｅｗａｖｅｅｑｕａｔｉｏｎｉｎｓｃｈａｌｌｏｗ ｗａｔｅｒ．ＪＭａｔｈＰｈｙｓ，１９９２， ３３（１２）：４３００－４３０５ １９ ＬｏｕＳＬ．ＳｉｍｉｌａｒｉｔｙｓｏｌｕｔｉｏｎｓｆｏｒｔｈｅＫａｄｏｍｓｅｖＰｅｔｖｉａｓｈｖｉｌｉｅｑｕａｔｉｏｎ．ＪＰｈｙｓＡ：ＭａｔｈＧｅｎ，１９９０，２３：６４９－６５４
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