国家自然科学基金(90503006)

作品数：9被引量：19H指数：2
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相关作者：高原焦小玉楼森岳更多>>
相关机构：复旦大学上海交通大学宁波大学更多>>
相关期刊：《Acta Mechanica Sinica》《Science China(Physics,Mechanics & Astronomy)》《Chinese Physics B》更多>>
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Approximate homotopy similarity reduction for the generalized Kawahara equation via Lie symmetry method and direct method被引量：1
《Chinese Physics B》2010年第8期28-34,共7页刘希忠 
Project supported by the National Natural Science Foundations of China(Grant Nos.10735030,10475055,10675065 and 90503006);the National Basic Research Program of China(Grant No.2007CB814800)
This paper studies the generalized Kawahara equation in terms of the approximate homotopy symmetry method and the approximate homotopy direct method. Using both methods it obtains the similarity reduction solutions an...
关键词：approximate homotopy symmetry method approximate homotopy direct method generalized Kawahara equation homotopy series solutions 
Some discussions about method for solving the variable separating nonlinear models
《Chinese Physics B》2010年第5期17-24,共8页阮航宇 
Project supported by the National Natural Science Foundation of China （Grant Nos. 10675065, 90503006 and 10735030） and the K.C.Wong Magna Fund in Ningbo University.Acknowledgement The author would like to thank the helpful discussion of Prof. Sen-Yue Lou.
Through analysing the exact solution of some nonlinear models, the role of the variable separating method in solving nonlinear equations is discussed. We find that rich solution structures of some special fields of th...
关键词：variable separating method nonzero seed solution nonlinear equation 
同伦近似对称法：六阶Boussinesq方程的同伦级数解被引量：4
《中国科学（G辑）》2009年第7期964-973,共10页焦小玉 高原 楼森岳 
国家自然科学基金(批准号:10735030,10475055,10675065,90503006);国家重点基础研究发展计划(编号:2007CB814800);长江学者和创新团队发展计划(编号:IRT0734);中国博士后科学基金(编号:20070410727);高等学校博士学科点专项科研基金(编号:20070248120)资助项目
提出了用以处理非线性问题的同伦近似对称法,并利用该方法研究流体动力学中的六阶Boussinesq方程.各阶相似约化解和各阶相似约化方程均可以写出通式,从而导出相应的同伦级数解.零阶相似约化方程等价于Painlevé IV型方程或Weierstrass...
关键词：同伦近似对称法 六阶Boussinesq方程 同伦级数解 
Variable coefficient nonlinear systems derived from an atmospheric dynamical system
《Chinese Physics B》2009年第11期4622-4635,共14页唐晓艳 高原 黄菲 楼森岳 
Project supported by the National Natural Science Foundation of China (Grant Nos 10735030, 10547124, 90503006 and 40305009);the National Basic Research Program of China (Grant Nos 2007CB814800 and 2005CB422301);Specialized Research Fund for the Doctoral Program of Higher Education (Grant No 20070248120);Program for Changjiang Scholars and Innovative Research Team in University (Grant No IRT0734);the Scientific Research Starting Foundation for Returned Overseas Chinese Scholars, Ministry of Education, China;the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No NCET-05-0591)
Variable coefficient nonlinear systems, the Korteweg de Vries （KdV）, the modified KdV （mKdV） and the nonlinear Schrǒdinger （NLS） type equations, are derived from the nonlinear inviscid barotropic nondivergent v...
关键词：nonlinear inviscid barotropic nondivergent vorticity equation variable coefficient equations non-auto-Bǎcklund transformation 
Approximate direct reduction method:infinite series reductions to the perturbed mKdV equation
《Chinese Physics B》2009年第9期3611-3615,共5页焦小玉 楼森岳 
supported by the National Natural Science Foundations of China (Grant Nos 10735030,10475055,10675065 and 90503006);National Basic Research Program of China (Grant No 2007CB814800);PCSIRT (Grant No IRT0734);the Research Fund of Postdoctoral of China (Grant No 20070410727);Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No 20070248120)
The approximate direct reduction method is applied to the perturbed mKdV equation with weak fourth order dispersion and weak dissipation. The similarity reduction solutions of different orders conform to formal cohere...
关键词：perturbed mKdV equation approximate direct reduction method series reduction solutions 
Approximate homotopy symmetry method:Homotopy series solutions to the sixth-order Boussinesq equation被引量：9
《Science China(Physics,Mechanics & Astronomy)》2009年第8期1169-1178,共10页JIAO XiaoYu1,GAO Yuan1 & LOU SenYue1,2,3 1 Department of Physics,Shanghai Jiao Tong University,Shanghai 200240,China 2 Department of Physics,Ningbo University,Ningbo 315211,China 3 School of Mathematics,Fudan University,Shanghai 200433,China 
Supported by the National Natural Science Foundation of China (Grant Nos. 10735030, 10475055, 10675065, and 90503006);the National Basic Research Pro-gram of China (Grant No. 2007CB814800);the Program for Changjiang Scholars and Innovative Research Team (Grant No. IRT0734);the Research Fund of Postdoctoral of China (Grant No. 20070410727);the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20070248120) Recommended by LIAO ShiJun
An approximate homotopy symmetry method for nonlinear problems is proposed and applied to the sixth-order Boussinesq equation,which arises from fluid dynamics.We summarize the general formulas for similarity reduction...
关键词：APPROXIMATE HOMOTOPY SYMMETRY method sixth-order BOUSSINESQ EQUATION HOMOTOPY series solutions 
Infinite series symmetry reduction solutions to the modified KdV-Burgers equation被引量：3
《Chinese Physics B》2009年第5期1821-1827,共7页姚若侠 焦小玉 楼森岳 
supported by the National Natural Science Foundations of China(Grant Nos 10735030,10475055,and 90503006);the National Basic Research Program of China(Grant No 2007CB814800);the Science Foundation for Post Doctorate Research from the Ministry of Science and Technology of China(Grant No 20070410727);the Natural Science Basic Research Plan in Shaanxi Province,China(Grant No SJ08A09)
From the point of view of approximate symmetry, the modified Korteweg-de Vries-Burgers （mKdV-Burgers） equation with weak dissipation is investigated. The symmetry of a system of the corresponding partial differentia...
关键词：modified Korteweg-de Vries-Burgers （mKdV-Burgers） equation approximate symme-try reduction series reduction solution 
Kac-Moody-Virasoro symmetry algebra of a (2+1)-dimensional bilinear system被引量：2
《Chinese Physics B》2008年第3期747-753,共7页李金花 楼森岳 
Project supported by the National Natural Science Foundation of China(Grant Nos10475055 and 90503006);the Science Research Fund of Zhejiang Provincial Education Department,China(Grant No20040969)
Based on some known facts of integrable models, this paper proposes a new （2＋1）-dimensional bilinear model equation. By virtue of the formal series symmetry approach, the new model is proved to be integrable becaus...
关键词：general symmetries Kac-Moody Virasoro symmetry algebra symmetry reduction 
Nonlinear excitations and“peakons”of a(2+1)-dimensional generalized Broer-Kaup system被引量：2
《Acta Mechanica Sinica》2007年第2期209-214,共6页X. Y. Tang K. W. Chow S. Y. Lou 
the National Natural Science Foundation of China (10475055,10547124 and 90503006);the Hong Kong Research Grant Council Contract HKU 7123/05E.
Shallow water waves and a host of long wave phenomena are commonly investigated by various models of nonlinear evolution equations. Examples include the Korteweg-de Vries, the Camassa-Holm, and the Whitham-Broer-Kaup ...
关键词：Shallow water wave .Excitation Broer-Kaup system .Peakon 
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