kdv方程论文文献综述

什么是渐近分析: 分层流体中的内孤立波的研究有重要的理论意义和实际意义,本文综述作者及其合作者近二十年来在内孤立波的渐近分析方面所做的工作.就研究对象而言,涉及KdV孤立波和非KdV孤立波(包括代数孤立波)及其相互作用;就研究方法而言,采用了各种摄动法(PLK方法、约化摄动法、多重尺度法、匹配法等)和它们相结合的形式,最近还利用了符号运算这一有力工具.我们发现,一般地说,首项解满足某种非线性发展方程(如KdV方程、gKdV方程、mKdV方程、Benjamin-Ono等),而高阶项则满足它们的线性化非齐次形式.幸运的是,可以求得摄动解的解析表达式.研究表明:渐近分析是研究内孤立波的有效途径,尤其是结合符号运算可以较系统地解决一大类问题,而且有解析结构清晰、计算工作量较小的优点.

主要出版论文目录 Ruguang Zhou, A Darboux transformation of the sl(2|1) super KdV hierarchy and a super lattice potential KdV equation, Phys. Lett. A 378 (2014) 1816-1819. Wei Fu, Da-Jun Zhang and Ruguang Zhou, A class of two-component Adler-Bobenko-Suris lattice equations, Chin. Phys. Lett. 31:9 (2014) 090202. Baoqiang Xia, Ruguang Zhou, Consecutive Rosochatius deformations of the Garnier system and the Henon-Heiles system, Abstract and Applied Analysis, 2014, Article ID 275450, 1-8. Baoqiang Xia, Ruguang Zhou, Consecutive Rosochatius deformations of the Neumann system, J. Math. Phys. 54:10 (2013) 103514 (10pp). Ying Xu and Ruguang Zhou, Integrable decompositions of a symmetric matrix Kaup–Newell equation and a symmetric matrix derivative nonlinear Schroeinger equation, Applied Math. Computation 219 (2013) 4551–4559. Shouting Chen, Ruguang Zhou, An integrable decomposition of the Manakov equation, Computational & Applied Mathematics, 31:1 (2012) 1-18. 周汝光，马文秀，王进利，双约束孤立子流的可积形变，数学年刊A, 32:2 (2011) 161-172. Ruguang Zhou, Ying Kui, Integrable fermionic extensions of the Garnier system and the anharmonic oscillator, Applied Mathematics and Computation, 217:22 (2011) 9261-9266. Baoqiang Xia, Ruguang Zhou, Conservation laws and symmetries for a nonholonomic deformed Volterra equation, J. Phys. A: Math. Theor. 44 :31 (2011) 315203(9pp) Junwei Cheng , Ruguang Zhou,Integrability and superintegrability of Toda symplectic map with multiple eigenparameters, Modern Physics Letters, 24:15 (2010) 1691-1696. Ruguang Zhou, The mixed Harry-Dym Soliton hierarchy, AIP conference proceeding 1212, Nonlinear and modern Mathematical physics: Proceedings of the first international workshop, Beijing (China), 15-21 July 2009, PP 170-174. Jing Zhao and Ruguang Zhou, An Integrable Symplectic Map Related to Discrete Nonlinear Schroedinger Equation,Communu. Theor. Phys., 53:5 (2010) 799-802. Ruguang Zhou, Mixed hierarchy of soliton equations, J. Math. Phys. 50:12 (2009) 123502 (12pp). Ruguang Zhou, Finite-Dimensional Integrable Hamiltonian Systems Related to the Nonlinear Schrödinger Equation, Studies in Applied Mathematics,123:4 (2009) 311-335. Xia Baoqiang and Ruguang Zhou, Integrable deformations of integrable symplectic maps, Phys. Lett. A, 373：47 (2009) 4360-4367. Xia Baoqiang and Ruguang Zhou, An integrable decomposition of defocusing nonlinear Schroedinger equation, Communu. Theor. Phys., 52:2 (2009) 203-205. Wen-Xiu Ma, Ruguang Zhou, and Liang Gao, Exact one-periodic and two periodic wave solutions to Hirota bilinear equations in (2+1) dimensions, Modern Physics Letters A, 24 (2009)1677-1688. Ruguang Zhou, Xiaoli Hu, From integrable to superintegrable, J. Phys. A: Math. Theor., 42 :17 (2009) 175401(9pp). Baoqiang Xia, Ruguang Zhou, An integrable decomposition of a model of dynamics of spinor Bose-Einstein condensates, Physics Letters A, 373:12-13 (2009) 1121-1129. Zhenyun Qin, Zixiang Zhou, Ruguang Zhou, Integrable Hamiltonian systems related to the AKNS system with matrix potentials, Modern Physics Letters B, 22：29 （2008), 2831-2842. Jilong Dai, Ruguang Zhou, Integrable Rosochatius deforamtions of the restricted cKdV flows,Chinese Phys. Letts., 25:9 (2008) 3095-3098. Ruguang Zhou, Zhenyun Qin, An integrable decomposition of the symmetric matrix KdV equation, Modern Physics Letters B, 22：13 （2008) 1307-1315. Jingsong He, Jing Yu, Yi Cheng, Ruguang Zhou,Binary nonlinearization of the super AKNS system, Modern Physics Letters B, 22：4 （2008), 275 - 288. Ruguang Zhou,Integrable Rosochatius deformations of the restricted soliton flows,J. Math. Phys. 48:10 (2007) 103510-10516. Ruguang Zhou, An integrable decomposition of the derivative nonlinear Schrödinger equation, Chinese Phys. Letts., 24:3 (2007) 589-591. Ruguang Zhou, Nonlinearizations of spectral problems of the nonlinear Schrödinger equation and the real-valued mKdV equation, J. Math. Phys.,48 (2007) 013510(9pp). Qiaoyun Jiang, Ruguang Zhou, Hierarchy of Combined TL-RTL Equations and an Associated (2+1)－Dimensional Lattice Equation, Comm. Theor. Phys., 46:5 (2006) 773-778. Jie Ji and Ruguang Zhou，Two types of new integrable decompositions of the Kaup–Newell equation，Chaos, Solitons & Fractals, 30:4 (2006) 993-1003 . Jing Yu, Ruguang Zhou, Two kinds of new integrable decompositions of the mKdV equation, Phys. Lett. A 349 (2006)452-461. Ruguang Zhou, Qiaoyun Jiang, A Darboux transformation and an exact solution for the relativistic Toda lattice equation, J. Phys. A: Math. Gen. 38 (2005)7735-7742. Zhenyun Qin , Ruguang Zhou, A (2+1)-dimensional breaking soliton equation associated with the Kaup-Newell soliton equation, Chaos, Solitons & Fractals, 21:2 (2004) 311-317. Ruguang Zhou, Relationships among three kinds of finite dimensional integrable Hamiltonian systems, Physica A, 320(2003) 128-140. Ruguang Zhou, A new (2+1)-dimensional integrable system and its algebro-geometric solution, IL Nuovo Cimento B, 117:8 (2002), 925-939. Wen-xiu Ma and Ruguang Zhou,Adjoint Symmetry Constraints of Multicomponent AKNS Equations, Chin. Ann. of Math., 23 B:3 (2002) 373-384. Wen-xiu Ma and Ruguang Zhou,Adjoint Symmetry Constraints Leading to Binary Nonlinearization, J. Nonlinear Math. Phys., 9: Supplement 1 (2002) 106-126. Wen-xiu Ma and Ruguang Zhou, Binary nonlinearization of spectral problems of the perturbation AKNS systems, Chaos, Solitons & Fractals, 13：7 (2002) 1451-1463. Wen-xiu Ma and Ruguang Zhou, Nonlinearization of spectral problems for the perturbation KdV systems, Physica A, 296/1-2, (2001) 60-74. Zixiang Zhou, Wenxiu Ma and Ruguang Zhou, Finite-dimensional integrable systems associated with the Davey-Stewartson I equation, Nonlinearity, 14：4 (2001) 701-717. Wenxiu Ma and Ruguang Zhou, On the relationship between classical Gaudin models and BC-type Gaudins models,J. Phys. A: Math. Gen. 34：4(2001)867-880. Ruguang Zhou and Wen-xiu Ma, Algebro-geometric solutions of the (2+1)-dimensional Gardner equation, IL Nuovo Cimento B, 115:2 (2000),1419-1431. Wenxiu Ma and Ruguang Zhou, Liouville integrability of perturbation systems of finite dimensional integrable Hamiltonian systems, Phys. Lett. A, 276: 1-4 (2000) 73-78. Ruguang Zhou and Zhijun Qiao, On the Restricted Toda and c-KdV flows of Neumann type, Commun. Theor. Phys. 34:2 (2000) 229-234. Ruguang Zhou, Wen-xiu Ma, Classical r-matrix structures of integrable mapping related to the Volterra lattice, Phys. Lett. A, 269：2-3 (2000) 103-111. Ruguang Zhou, W.X. Ma, The r-matrix structure of the restricted coupled AKNS-Kaup-Newell flow, Appl. Math. Lett. 13:3 (2000) 131-135. Ruguang Zhou, The restricted Boussinesq flows, their Lax representations and r-matrix, Commun. Theor. Phys. 33:1 (2000) 75-80. Wen-xiu Ma, Ruguang Zhou, A coupled AKNS-Kaup-Newell soliton hierarchy, J. Math. Phys. 40:9 (1999) 4419-4428. Wen-xiu Ma, Ruguang Zhou,On inverse recursion operator and tri-Hamiltonian formulation for a Kaup-Newell system of DNLS equations, J. Phys. A: Math. Gen. 32：20 (1999) L239-242. Ruguang Zhou, Lax representation, r-matrix method, and separation of variables for Neumann-type restricted flow, J. Math. Phys. 39：5 (1998), 2848-2858. Ruguang Zhou and Wen-xiu Ma, New classical and quantum integrable systems related to MKdV integrable hierarchy, J. Phys. Soc. Japan 67：12 (1998) 4045-4050. Ruguang Zhou, r-Matrix for the restricted KdV flows with the Neumann constraints, J. Nonlinear Math. Phys. 5：2 (1998) 228-234. 周汝光，一个求孤子方程有限带势解的方法，数学物理学报，18：2（1998）228-234.（英文翻译成：Ruguang Zhou, A method for finding finite-band solutions of soliton equations, Acta Math. Sci. (Chinese) 18：2 (1998) 228-234.） 周汝光, Neumann型约束Tu流的r矩阵和分离变量,数学年刊A辑,19A:4 (1998) 463-468.英文版Ruguang Zhou, The r-matrix and separability of variables for restricted Tu flow with the Neumann constraint, Chinese Journal of Contemporary Mathematics, 19:3 (1998) 277-284. Chunping Liu, Ruguang Zhou and Mingru Zhou, A simple method to construct the traveling wave solutions to nonlinear evolution equations, Phys. Lett. A 246：1-2 (1998) 113-116. Ruguang Zhou, Generalized confocal involution system and some kinds of eigenvalue problem, Phys. Lett. A,184 (1993) 71-73. Ruguang Zhou, Hierarchy of negative order equation and its Lax pair, J. Math. Phys.36 (1995) 4220-4225. Ruguang Zhou, Dynamical r-matrices for the constrained Harry-Dym flows, Phys. Letts. A 220 (1996) 320-330. Zhijun Qiao and Ruguang Zhou, Discrete and continuous finite-dimensional integrable systems possessing the same nondynamical r-matrix, Phys. Lett. A, 235 (1997) 35-40. Ruguang Zhou, The finite-band solution of Jaulent-Miodek equation. J. Math. Phys. 38：5 (1997) 2335-2546.