无穷格点上长波-短波共振方程组核截面的分形维数估计
Finite Fractal Dimension of Kernel Sections for Long-Wave-Short-Wave Resonance Equations on Infinite Lattices
摘要
该文证明了无穷格点上长波-短波共振方程组核截面的分形维数估计.
This paper proves an upper bound of fractal dimension of the kernel sections for the long-wave-short-wave resonance equations on infinite lattices.
出处
《数学物理学报(A辑)》
CSCD
北大核心
2015年第6期1146-1157,共12页
Acta Mathematica Scientia
基金
国家自然科学基金(11271290
51279202
31370381)
国家重点基础研究发展计划(973)项目(2015CB057905)资助
关键词
格点长波-短波共振方程组
核截面
分形维数.
Lattice long-wave-short-wave resonance equations
Kernel sections
Fractal dimension.
参考文献52
-
1Ahmed Abdallah Y. Exponential attractors for first-order lattice dynamical systems. J Math Anal Appl, 2008, 839:217-224. 被引量:1
-
2Ahmed Abdallah Y. Uniform exponential attractors for second order non-autonomous lattice dynamical systems. Comm pure Appl Anal, 2009, 8:803-813. 被引量:1
-
3Angulo J, Montenegro J F B. Existence and evenness of solitary-wave solutions for an equation of short and long dispersive waves. Nonlinearity, 2000, 13:1595-1611. 被引量:1
-
4Benney D J. A general theory for interactions between short and long waves. Stud Appl Math, 1977, 56: 81-94. 被引量:1
-
5Bekiranov D, Ogawa T, Ponce G. On the well-posedness of Benney's interaction equation of short and long waves. Adv Differential Equations, 1996, 1:919-937. 被引量:1
-
6Bekiranov D, Ogawa T, Ponce G. Interation equations for short and long dispersive waves. J Funct Anal, 1998, 158:357-388. 被引量:1
-
7Beyn W J, Pilyugin S Yu. Attractors of reaction diffusion systems on infinite lattices. J Dyna Differential Equations, 2003, 15:485-515. 被引量:1
-
8Bates P W, Chen X, Chmaj A. Traveling waves of bistable dynamics on a lattice. SIAM J Math Anal, 2003, 35:520-546. 被引量:1
-
9Bates P W, Lisei H, Lu K. Attractors for stochastic lattice dynamical systems. Stoch Dyna, 2006, 6:1 -21. 被引量:1
-
10Chepyzhov V V, Vishik M I. Attractors for Equations of Mathematical Physics. Providence, RI: Amer Math Soc. 2002. 被引量:1
二级参考文献36
-
1Chate H,Courbage M. Lattice systems[J].Physical Review D,1997.1-612. 被引量:1
-
2Chow S N. Lattice Dynamical Systems.Lecture Notes in Math,1822[M].Beilin:Springer-Verlag,2003. 被引量:1
-
3Keener J P. Propagation and its failure in coupled systems of discrete excitable cells[J].SIAM Journal of Applied Mathematics,1987.556572. 被引量:1
-
4Erneux T,Nicolis G. Propagating waves in discrete bistable reaction diffusion systems[J].Physical Review D,1993.237-244. 被引量:1
-
5Kapval R. Discrete models for chemically reacting systems[J].Journal of Mathematical Chemistry,1991.113163. 被引量:1
-
6Chow S N,Mallet-Paret J. Pattern formation and spatial chaos in lattice dynamical systems[J].IEEE Transactions on Circuits and Systems,1995.746751. 被引量:1
-
7Fabiny L,Colet P,Roy R. Coherence and phase dynamics of spatially coupled solid-state lasers[J].Physical Review A,1993.42874296. 被引量:1
-
8Hillert M. A solid-solution model for inhonogeneous systems[J].Acta Metallurgica,1961.525535. 被引量:1
-
9Chua L O,Roska T. The CNN paradigm[J].IEEE Transactions on Circuits and Systems,1993.147156. 被引量:1
-
10Chua L O,Yang Y. Cellular neural networks:theory[J].IEEE Transactions on Circuits and Systems,1988,(10):12571272.doi:10.1109/31.7600. 被引量:1
-
1黄煜.具阻尼的非线性波动方程整体吸引子的Hausdorff维数、分形维数估计[J].应用数学学报,1998,21(2):257-266. 被引量:3
-
2徐桂琼,郁志清.Lienard方程的新双周期解及其应用[J].应用数学与计算数学学报,2015,29(4):463-472. 被引量:1
-
3瞿成勤,周作领.黎曼流形上不变集的分形维数估计[J].数学学报(中文版),2004,47(1):51-58.
-
4罗宏,蒲志林.Extended Fisher-Kolmogorov系统的整体吸引子及其分形维数估计[J].四川师范大学学报(自然科学版),2004,27(2):135-138. 被引量:3
-
5殷朝阳,丁伟.Sobolev-Lieb-Thirring不等式的推广及其在非自治无穷维动力系统中的应用[J].中山大学学报(自然科学版),2001,40(4):24-27.
-
6黄文华,张解放,等.Coherent soliton structures of the (2+1)—dimensional long—wave—short—wave resonance interaction equation[J].Chinese Physics B,2002,11(11):1101-1105. 被引量:6
-
7李红达,叶正麟,彭国华.Cantor尘的Hausdorff测度估计[J].计算数学,2002,24(3):265-272.
-
8何树红.一类广义Navier-Stokes方程的整体吸引子及其维数估计[J].河南师范大学学报(自然科学版),2000,28(1):16-20.
-
9Wei-xiang Sun,Li-zhen Huang,Yan-rui Yang,Xin-xing Liu,童真.Large Amplitude Oscillatory Shear Studies on the Strain-stiffening Behavior of Gelatin Gels[J].Chinese Journal of Polymer Science,2015,33(1):70-83.