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经典物理学和量子理论
  • 项目名称：经典物理学和量子理论
  • 项目类别：国家杰出青年科学基金
  • 批准号：19925522
  • 申请代码：A050102
  • 项目来源：国家自然科学基金
  • 研究期限：2000-01-01-2003-12-31
  • 项目负责人：楼森岳
  • 负责人职称：教授
  • 依托单位：上海交通大学
  • 批准年度：1999
中文摘要：

在非线性科学研究中以对称性研究为中心，在可积体系理论中，建立了1＋1维可积体系的强对称算子的因式化和逆方法；建立了2＋1维要积模型的形式级数对称方法，建立了无穷多Lax对和非局域对称理论；给出了多种意义下的高维可积模型；完善和推广了对称性约化的直接法。给出了希格斯粒子质量估计。在实验上发现了双原子格点体系的能隙孤子等。在SCI系统发表了论文一百余篇。1997年在SCI系统论文数名列全国第二，被引用篇数名列全国第一。

中文主题词： 分离变量法；对称性；局域激发；孤子、混沌和分形；可积系统；
结论摘要：

英文主题词Variable separation approach; symmetries; localized excitations; solitons, chaos and fractals; integrable systems

成果综合统计
成果类型
数量
  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
  • 134
  • 7
  • 0
  • 0
  • 0
期刊论文
Revisitation of the localized excitations of the 2 1 dimensional KdV equarion,
A new generalization of the (2 1)-dimensional Davey-Stewartson equation
Conditional similarity solution of the Boussinesq equation
On the coherent structures of Nizhnik-Novikov-Veselov equation
Symmtry analysis and exact solutions of? the 2 1 dimensional sine-Gordon system
Deforming the lower-dimensional solitons to higher-dimensional ones
Painlev?integrability and multi- dromion solutions of the 2 1 dimensional AKNS system
High dimensional Virasoro integrable models and exact solutions
Abundant Coherent Structures of the (2 1)-dimensional Broer-Kaup- Kupershmidt Equation,
Obtain lower dimensional turbulence systems from higher dimensional Lax integrable models
Self-steepening and third order dispersion induced optical solitons in fiber
Higher dimensional integrable models with infinitely dimensional Virasoro type symmetry algebra
Conditional Similarity Reduction Approach: Jimbo-Miwa equation
Multi-soliton Solutions of the Konopelchenko-Dubrovsky Equation
Similarity and conditional similarity reductions of a (2 1)-dimensional KdV equation via a direct me
Higher dimensional integrable models from lower?ones via Miura type deformation relation
(3 1)- dimensional integrable models with infinitely dimensional Virasoro type symmetry algebra and
High dimensional Schwartz KP equations
Some special types of multisoliton solutions of the Nizhnik-Novikov- Vesselov equation
Localized exicitations in (2 1)- dimensional systems
Dromions, dromions lattice, breathers and instantons of the Davey-Stewartson equation
(2 1)-dimensional (M N)-component AKNS system: Painlev?integrability, infinitely many symmetries and
Symmetry analysis of the (2 1)- dimensional nonlinear Klein-Gordon equations,
Characteristic manifold and Painlev?integrability: Fifth order Schwarzian KdV type equation
High dimensional Schwarzian deriva- tives and Painlev?integrable models
Conditional similarity solutions of (2 1)-dimensional generalnonintegrable KdV equation
Solutions of (2 1)-Dimensional Dispersive Long Wave equation
(2 1)-dimensional compacton solutions with and without completely elastic interaction properties,
Painlev?analysis and special solutions of generalized Broer–Kaup equations,
Higher dimensional peculiar Lax pairs for lower dimensional chaos and turbulence systems
Abundant coherent structures of the dispersive long-wave equation in (2 1)-dimensional spaces
Painleve Integrability and Abundant Localized Structures of (2 1)-dimensional Higher-Order Broer-Kau
Quintic nonlinearity induced solitary waves in plasma physics,
Localized solutions with chaotic and fractal behaviours in a (2 1)-dimensional dispersive long-wav
Fractal solutions of the Nizhnik- Novikov-Veselov equation,
Adomian decomposition method and exact solutions of the perturbed-KDV Equation
Dromion and Multi-soliton Structures of the (2 1)-dimensional Higher-Order Broer-Kaup System
Mapping deformation method and its application to nonlinear equations
The exact solutions of some (2 1)- dimensional integrable systems
Multisoliton solutions of the (3 1)-dimensional Nizhnik-Novikov-Veselov equation
The soliton solutions and periodic solutions of (3 1)-dimensional Nizhnik-Novikov-Veselov equation
Variable separation and exact solutions to generalized nonlinear diffusion equations
Virasoro structure and localized excitations of the LKR system,
Rich localized coherent structures of the (2 1)-dimensional BKK equation
Conditional similarity reductions of Jimbo-Miwa equation via the classical Lie group approach
New variable separation approach: application to nonlinear diffusion equations
Localized excitations of the (2 1)-dimensional sine-Gordon system,
What will happen when a dromion meets with a ghoston
Extended multilinear variable separation approach and multivalued localized excitations for some (2
Multilinear variable separation approach in (3 1)-dimensions: the Burgers equation,
The interactions of localized coherent structures for a (2 1)-dimensional system,
Soliton excitations and periodic waves without dispersion relation in shallow water system,
A new kind of localized excitations for a large class of (2 1)-dimensional systems
Variable separation solutions for the (2 1)-dimensional Burgers equations,
(1 1)-dimensional turbulent and chaotic systems reduced from (2 1)-dimensional Lax integrable disper
Variable Separation and Derivative- dependent Functional Separable Solutions to Generalized KdV Equa
Exact solutions of nonlinear dynamics equation in a new double-chain model of DNA
Folded Solitary Waves and Foldons in (2 1) Dimensions,
Darboux transformation and variable separation approach: the Nizhnik-Novikov-Veselov equation,
High-Dimensional Integrable Models with Conformal Invariance,
Rich localized coherent structures of the (2 1)-dimensional Broer-Kaup- Kupershmidt equation
An extension of mapping deformation method and new exact solution for three coupled nonlinear partia
Solitary wave solutions for a general Boussinesq type fluid model.
Lie Point Symmetries of Differential- Difference Equations,
Derivative-dependent functional separable solutions for the KdV-type equations
Symmetrys and strong symmetries of the 3 1 dimensional Burgers equation
Analytical investigation of Rossby waves in atmospheric dynamics
Variable separation approach for a differential-difference system: special Toda equation.
Soliton fission and fusion: Burgers equation and Sharma-Tasso-Olver equation
Variable separation and derivative- dependent functional separable solutions to generalized nonlinea
Fission and fusion of localized coherent structures for a (2 1)-dimensional KdV equation
Equations of arbitrary order invariant under the Kadomtsev-Petviashvili symmetry group
A variable separation approach for integrable and nonintegrable models: coherent structures of 2 1 d
会议论文
A new kind of localized excitations for a large class of (2 1)-dimensional systems
Localized Excitations in (2 1) Dimensional systems
Rich localized coherent structures of the (2 1)-dimensional BKK equation
2 1维可积系统的局域激发
任意非线性系统的Lax对
Nonlocal Symmetries of Nonlinear Integrable Models
Group explanation for the conditional similarity reductionsof the (2 1)-dimensional KdV equation
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