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灾害性天气和气候研究的数学物理问题
  • 项目名称：灾害性天气和气候研究的数学物理问题
  • 项目类别：重点项目
  • 批准号：10735030
  • 申请代码：A050101
  • 项目来源：国家自然科学基金
  • 研究期限：2008-01-01-2011-12-31
  • 项目负责人：楼森岳
  • 负责人职称：教授
  • 依托单位：宁波大学
  • 批准年度：2007
中文摘要：

自然灾害对生态环境、基础设施、人类社会造成的破坏越来越大。我国每年由此而损失2000 亿元左右。本项目针对灾害性天气和气候的预测和形成机理以及当前国际非线性数学物理的前沿发展情况，建立了一些有实际意义的非线性模型，如描述台风三维立体结构的同伦模型，多涡相互作用模型，耦合可积系统模型以及大量的离散可积系统等等。在方法方面，建立了一些与灾害问题直接有关的非线性物理问题研究的新方法，如近似对称微扰理论，线性同伦近似对称微扰理论，最不敏感非线性同伦方法，代数恒等式方法，角平分线定理的指标齐次分解，非局域对称方法等等。将新建立研究方法应用于实际物理问题和模型，得到了许多有意义的严格解和可能的实际应用。如有些解可以成功描述台风的立体结构、引导气流与台风中心的关系、双眼壁台风、雪灾和洪涝灾害相关的大气阻塞、双台风的藤原效应、台风的吞并或排斥、极涡鞍型场、海啸孤波与周期背景场的相互作用等等。

中文主题词： 灾害性天气气候；非线性数学物理方程；对称性；扰动理论；台风结构
结论摘要：

英文主题词Disastrous weather and climate; nonlinear equations of mathematical physics; symmetries; perturbation theory; typhoon structure

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
  • 168
  • 2
  • 0
  • 2
  • 0
期刊论文
Bright soliton solution in 1D tonks-girardeau gas
Nonsingular travelling complexiton soloutions to a coupled korteweg-de vries equation
An integrable coupled hybrid lattice and its exact solutions
Lie symmetry groups of (2+1)-dimensional BKP equation and its new solutions
A maple package to compute lie symmetry groups and symmetry reductions of (1+1)-dimensional nonlinea
用同伦扰动方法研究复KdV方程的数值复数解
用直接法研究非等谱KP方程的相似约化
时间离散的超混沌系统的函数摄影同步
修正KP方程的两元达布变换
(2+1)维多元素的 Broer Kaup 系统的相似约化
奇次高阶薛定谔方程的广义的子方程展开法和解析解
带有未知参数的函数级联同步方法及其应用
一类带有任意阶非线性项的非线性发展方程的数值解
用同伦摄动方法研究一类带参数导数的耦合非线性方程
一般Davey–Stewartson系统的对称，完全对称群和精确解
一类新的分式耦合非线性方程的数值解
Kac-Moody-Virasoro symmetry algebra of a (2+1)-dimensional bilinear system
一个带自相溶源的超可积方程族及其守恒律
一种研究非等谱和变系数修正KdV方程可积性的直接方法
一个一般KP方程的贝克隆变换和解
南海夏季风爆发与西北太平洋热带气旋活动
（2+1）维扩散长波方程的对称约化、精确解和守恒律
直接方法求解广义（2+1）维Sasa–Satsuma的对称和精确解
时间离散混沌系统的自适应功能投影同步
时间离散超混沌系统的级联同步方案功能。
不确定参数的时间离散混沌系统的投影同步功能
（2+1）维立方非线性 schrodinger方程的有限对称变换群和一些精确解
A new (2+1)-dimensional supersymmetric Boussinesq equation and its Lie symmetry study
一类耦合非线性Schrdinger方程的Painlevé性质、严格解及其在大气重力波中的应用
Symmetries and Algebras of a (2+1)-Dimensional MKdV-Type System
Lie Point Symmetries and Exact Solutions of the Coupled Volterra System
Conservation laws of equation family with same Kac-Moody-Virasoro symmetry
A class of coupled nonlinear Schrodinger equations: Painlev, property, exact solutions, and applicat
Climate control of the global tropical storm days (1965-2008)
由斜压位涡方程推导出的3类广义的KP方程
一个新的4维混沌系统
（2+1）维的非线性正压和准地转势涡方程贝克隆变换和精确解
非等谱BKP方程的全体对称群，潘勒威性和精确解
Super typhoon activity over the western North Pacific and its relationship with ENSO.
带任意阶不变量的（2+1）维扩散长波方程的Kac-Moody-Virasoro对称代数
直接方法求解非奇次高阶非线性Schrodinger方程
（3+1）维的非线性斜压位涡方程的对称分析和精确解
四场格Blaszak-Marciniak 方程的对称约化和精确解
印度洋-太平洋海表温度年际变化的联合模态
(3+1)维Zakharov–Kuznetsov方程的对称约化和精确解
Constraints and Soliton Solutions for KdV Hierarchy and AKNS Hierarchy
Integrable KP Coupling and Its Exact Solution
Exact solutions of (2+1)-dimensional Euler equation found by weak Darboux transformation
Relation between the induced flow and the position of typhoon: Chanchu 2006
南海土台风生成及发展过程海气热通量交换特征
北大西洋涛动指数变化与北半球冬季阻塞活动
(2+1）维共振 Davey-Stewartson 系统的完全对称群及相似约化
广义5阶KdV方程的伪势、Lax对和Backlund变换
复KdV方程的数值复解
Doubly periodic patterns of modulated hydrodynamic waves:exact solutions of the Davey-Stewartson sys
Lie Point Symmetry Algebras and Finite Transformation Groups of Baroclinic Mode for Rotating Stratif
Shocks, explosions, and vortices in two-dimensional homogeneous quantum magnetoplasma
Drift shocks, explosions and vortices in inhomogeneous quantum magnetoplasma
Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics
Dark Parameterizations, Equivalent Partner Fields and Integrable Systems
变系数的KdV方程的延长结构
大气中双层模型的对称约化及精确解
双Bell多项式应用到广义Nizhnik–Novikov–Veselov方程
(2+1)-维非线性发展方程的双Bell多项式应用及精确周期波解。
Qiao方程的延长结构
Extension of variable separable solutions for nonlinear evolution equations
A (2+1)-dimensional displacement shallow water wave system
Coupled Nonlinear Schrodinger Equation: Symmetries and Exact Solutions
Analytical Solitary Wave Solutions to a (3+1)-Dimensional Gross-Pitaevskii Equation with Variable Co
Approximate Symmetry Reduction Approach: Infinite Series Reductions to the KdV-Burgers Equation
Infinite series symmetry reduction solutions to the modified KdV-Burgers equation
非线性格方程的ADM-Padé策略
Konopelchenko–Dubrovsky方程的有限对称变换群和精确解
广义Nizhnik Novikov Veselov方程的对称约化和精确解。
广义洛伦兹规范形式和Rossler系统之间的广义Q-S同步
含有未知参数的时间离散混沌系统的预期功能同步
两类（2+1）维非线性Klein–Gordon方程的对称分析
关于一类非线性偏微分方程的非经典对称和和兼容性的注意
2维时间离散混沌系统的自适应控制和功能投影同步
（2+1）维非线性Klein–Gordon方程的二维对称约化
分数阶广义洛伦兹规范形式的混沌
(2+1)-维广义Calogero-Bogoyavlenskii-Schiff方程的无穷多对称及其约化
微分差分方程的Adomian分解法和padé近似
西北太平洋超强台风活动特征及其与ENSO的关系
二维离散洛伦兹混沌系统和三维离散的rossler超混沌系统的稳定性
Nonsensitive Homotopy-Pade Approach: Anharmonic Oscillators
Multi-linear variable separation approach to nonlinear systems
Monopole Blocking Governed by a Modified KdV Type Equation
Approximate Symmetry Reduction to the Perturbed One-Dimensional Nonlinear Schrodinger Equation
Nonsensitive Nonlinear Homotopy Approach
Approximate Homotopy Direct Reduction Method: Infinite Series Reductions to Perturbed mKdV Equations
Bright Soliton Solutions in Degenerate Femi Gas near Feshbach Resonance
Approximate Symmetry Reduction and Infinite Series Solutions to the Nonlinear Wave Equation with Dam
Approximate direct reduction method: infinite series reductions to the perturbed mKdV equation
同伦近似对称法:六阶Boussinesq方程的同伦级数解
Approximate Symmetries and Infinite Series Symmetry Reduction Solutions to Perturbed Kuramoto-Sivash
Localized Waves in Nonlinear Systems with Spatially Inhomogeneous Nonlinearity
Variable coefficient nonlinear systems derived from an atmospheric dynamical system
中国东部海区经向热力差异对夏季南京气候变化的影响
远场模型方程的同伦近似对称约化
Full symmetry groups and similar reductions of a (2+1)-dimensional resonant Davey-Stewartson system
Prolongation structure of the equation studied by Qiao
黄河流域降水异常与渤、黄海水温,大气环流异常变化及入海流量关系的研究
Binary bell polynomials Approach to generalized Nizhnik-Novikov-Veselov equation
A discrete Lax-integrable coupled system related to coupled KdV and coupled mKdV equations
Different discrete soliton states in periodic optical induced waveguide lattice
Approximate generalized conditional symmetries for perturbed evolution equations
Lax pair and exact solutions of a discrete coupled system related to coupled KdV and coupled mKdV eq
Functional variable separation for extended nonlinear elliptic equations
On exact solutions of a coupled Korteweg-de Vries system
截断Painleve展开：一个寻求2+1维非线性系统严格解和Dromion相互作用的统一方法
2＋1维广义Calogero-Bogoyavlenskii-Schiff方程的无穷多对称及其约化
超奇异的Marcinkiewicz积分交换子的有界性
离散修正KdV方程的解析近似解
Symmetry Analysis of Two Types of （2＋1）-Dimensional Nonlinear Klein-Gorden Equation
Symmetry reduction and exact solutions of the （3＋ 1）-dimensional Zakharov-Kuznetsov equation
Symmetry analysis and explicit solutions of the （3＋1）-dimensional baroclinic potential vorticity equation
Analytic Approximations for Soliton Solutions of Short-Wave Models for Camassa-Holm and Degasperis-Procesi Equations
Sinh-Gordon方程的同伦近似解
一类耦合非线性Schrdinger方程的Painlevé性质、严格解及其在大气重力波中的应用
Approximate Homotopy Symmetry Reduction Method： Infinite Series Reductions to Kawahara Equation
Finite Symmetry Transformation Groups and Some Exact Solutions to （2＋1）-Dimensional Cubic Nonlinear SchrSdinger Equantion
An Extension of Algorithm on Symbolic Computations of Conserved Densities for High-Dimensional Nonlinear Systems
Approximate homotopy similarity reduction for the generalized Kawahara equation via Lie symmetry method and direct method
A new （2＋1）-dimensional supersymmetric Boussinesq equation and its Lie symmetry study
An Elastic Interaction Model of Vortices
Symmetry Analysis and Similarity Solutions of a Resonant Davey-Stewartson System
Similarity Reductions of Nonisospectral KP Equation by a Direct Method
非线性Landou-Ginburg-Higgss方程的解析解
一个3＋1维非线性发展方程和Maccari系统的对称群及精确解
一类偏微分方程的Painleve分析
寻找变系数KP方程的精确解
群理论解非线性KdV方程的探讨
一个3+1维非线性发展方程和Maccari系统的对称群及精确解(英文)
一些非传播孤立子实验和相关理论
Three types of generalized Kadomtsev-Petviashvili equations arising from baroclinic potential vorticity equation
Adomian decomposition method and Pade approximants for solving the Blaszak-Marciniak lattice
Some Similarity Reduction Solutions to Two-Dimensional Incompressible Navier-Stokes Equation
A Maple Package on Symbolic Computation of Hirota Bilinear Form for Nonlinear Equations
Analytical Solitary Wave Solutions to a （3＋1）-Dimensional Gross-Pitaevskii Equation with Variable Coefficients
Approximate direct reduction method： infinite series reductions to the perturbed mKdV equation
Some discussions about method for solving the variable separating nonlinear models
Approximate Symmetries and Infinite Series Symmetry Reduction Solutions to Perturbed Kuramoto-Sivashinsky Equation
Infinite series symmetry reduction solutions to the modified KdV-Burgers equation
Variable coefficient nonlinear systems derived from an atmospheric dynamical system
Backlund Transformations and Explicit Solutions of （2d-1）-Dimensional Barotropic and Quasi-Geostrophic Potential Vorticity Equation
Matter-Wave Solitons in Two-Dimensional Bose-Einstein Condensates with Time-Dependent Scattering Length in a Harmonic Trap
Symmetry and Exact Solutions of （2＋1）-Dimensional Generalized Sasa-Satsuma Equation via a Modified Direct Method
A Note on Nonclassical Symmetries of a Class of Nonlinear Partial Differential Equations and Compatibility
Adomian Decomposition Method and Pade Approximants for Nonlinear Differential-Difference Equations
Kac-Moody-Virasoro Symmetry Algebra of （2＋1）-Dimensional Dispersive Long-Wave Equation with Arbitrary Order Invariant
Numerical Solutions of a New Type of Fractional Coupled Nonlinear Equations
Symmetry Reductions and Exact Solutions of Blaszak-Marciniak Four-Field Lattice Equation
Binary Bell Polynomials, Bilinear Approach to Exact Periodic Wave Solutions of (2 l 1)-Dimensional Nonlinear Evolution Equations
Approximate solution for the Klein-Gordon-SchrSdinger equation by the homotopy analysis method
Similarity Reductions of Nonisospectral BKP Equation
Symmetry and general symmetry groups of the coupled Kadomtsev-Petviashvili equation
Approximate Similarity Reduction for Perturbed Kaup-Kupershmidt Equation via Lie Symmetry Method and Direct Method
会议论文
Kac-Moody-Virasoro Symmetries and Related Conservation Laws
带有时间和空间分式导数的耦合Burgers方程的数值解
获奖
第九届山东省青年科技奖
第九届山东省青年科技奖
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