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非线性耦合Drinfeld-Sokolov-Satsuma-Hirota方程的对称约化
  • ISSN号：1007-6735
  • 期刊名称：《上海理工大学学报》
  • 时间：0
  • 分类：O175[理学—数学;理学—基础数学]
  • 作者机构：上海理工大学理学院,上海200093
  • 相关基金：国家自然科学基金资助项目（11071164,11201302）;上海市自然科学基金资助项目（10ZR1420800）;上海市重点学科建设资助项目（XTKX2012）
作者： 牛莉莉, 胡恒春
关键词： 对称约化, 非线性耦合Drinfeld-Sokolov-Satsuma-Hirota方程, Clarkson-Kruskal直接法, symmetry reduction, nonlinear coupled Drinfeld-Sokolov-Satsuma-Hirota equation, Clarkson-Kruskal direct method
中文摘要：

由Clarkson和Kruskal提出的Clarkson-Kruskal直接法是一种不涉及群运算的求解非线性偏微分方程的代数方法,不同于经典李群方法,Clarkson-Kruskal直接法不需要求解复杂的初值问题.应用Clarkson-Kruskal直接法,并且利用相应规则得到非线性耦合Drinfeld-Sokolov-Satsuma-Hirota方程的对称约化.同时进一步求得了Drinfeld-Sokolov-Satsuma-Hirota方程新的相似变量和相似解,并与经典李群方法得到的结果进行对比,验证了Clarkson-Kruskal直接法与经典李群方法得到的结果可以互相变换.

英文摘要：

The Clarkson-Kruskal direct method was proposed by Clarkson and Kruskal,which is an algebraic method for solving nonlinear partial differential equations.The advantage of this method is that it does not involve group theory operations and complex initial value problems.It can give new similarity solutions of the nonlinear evolution equations which could not be obtained by the classical Lie group method and the nonclassical Lie group method.By using the Clarkson-Kruskal method and corresponding rules,the symmetry reduction and the similarity transformation of the Drinfeld-Sokolov-Satsuma-Hirota equation were obtained.It is verified that the results by the Clarkson-Kruskal method can be transformed into those by the classical Lie group method.

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期刊信息
  • 《上海理工大学学报》
  • 北大核心期刊（2011版）
  • 主管单位:上海市教育委员会
  • 主办单位:上海理工大学
  • 主编：庄松林
  • 地址：上海市军工路516号489信箱
  • 邮编：200093
  • 邮箱：xbzrb@USST.edu.cn
  • 电话：021-55277251
  • 国际标准刊号：ISSN：1007-6735
  • 国内统一刊号：ISSN：31-1739/T
  • 邮发代号:4-401
  • 获奖情况:
  • 上海市高等学校优秀自然科学学报一等奖,1999年获全国优秀高等学校自然科学学报及教育部优...,1995年获机械工业部优秀科技期刊三等奖
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国化学文摘（网络版）,荷兰文摘与引文数据库,美国剑桥科学文摘,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）
  • 被引量:5359