A FAMILY OF INTEGRABLE SYSTEMS OF LIOUVILLE AND LAX REPRESENTATION, DARBOUX TRANSFORMATIONS FOR ITS CONSTRAINED FLOWS

Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (1): 26-34.

A FAMILY OF INTEGRABLE SYSTEMS OF LIOUVILLE AND LAX REPRESENTATION, DARBOUX TRANSFORMATIONS FOR ITS CONSTRAINED FLOWS

张玉峰^1,2, 张鸿庆²

1. Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China;
2. Basic Courses Department, Shandong University of Science and Technology, Tai’an, Shangdong 271019, P. R. China

收稿日期:2000-10-16 修回日期:2001-09-28 出版日期:2002-01-18 发布日期:2002-01-18
基金资助:
the Chinese Basic Research "Mathematical Mechanization and a Platform for Automated Reasoning"(G1998030600)

A FAMILY OF INTEGRABLE SYSTEMS OF LIOUVILLE AND LAX REPRESENTATION, DARBOUX TRANSFORMATIONS FOR ITS CONSTRAINED FLOWS

ZHANG Yu-feng^1,2, ZHANG Hong-qing²

1. Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China;
2. Basic Courses Department, Shandong University of Science and Technology, Tai’an, Shangdong 271019, P. R. China

Received:2000-10-16 Revised:2001-09-28 Online:2002-01-18 Published:2002-01-18
Supported by:
the Chinese Basic Research "Mathematical Mechanization and a Platform for Automated Reasoning"(G1998030600)

摘要/Abstract

摘要： A family of integrable systems of Liouville are obtained by Tu pattern. Using higher-order potential-eigenfunction constraints, the integrable systems are factorized to two x- and t_n-integrable Hamiltonian systems whose Lax representation and three kinds of Darboux transformations are presented.

中图分类号:

O175.29

张玉峰;张鸿庆. A FAMILY OF INTEGRABLE SYSTEMS OF LIOUVILLE AND LAX REPRESENTATION, DARBOUX TRANSFORMATIONS FOR ITS CONSTRAINED FLOWS[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(1): 26-34.

ZHANG Yu-feng;ZHANG Hong-qing. A FAMILY OF INTEGRABLE SYSTEMS OF LIOUVILLE AND LAX REPRESENTATION, DARBOUX TRANSFORMATIONS FOR ITS CONSTRAINED FLOWS[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(1): 26-34.

[1]	张乔夫;崔俊芝. Existence theory for Rosseland equation and its homogenized equation[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(12): 1595-1612.
[2]	赖绍永;胡青龙. THE ASYMPTOTIC THEORY OF INITIAL VALUE PROBLEMS FOR SEMILINEAR PERTURBED WAVE EQUATIONS IN TWO SPACE DIMENSIONS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(1): 82-91.
[3]	陈勇;郑宇;张鸿庆. THE HAMILTONIAN EQUATIONS IN SOME MATHEMATICS AND PHYSICS PROBLEMS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(1): 22-27.
[4]	张兴武;武际可;朱海平;黄克服. GENERALIZED CANONICAL TRANSFORMATION AND SYMPLECTIC ALGORITHM OF THE AUTONOMOUS BIRKHOFFIAN SYSTEMS[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(9): 1029-1034.
[5]	闫振亚;张鸿庆. AUTO-DARBOUX TRANSFORMATION AND EXACT SOLUTIONS OF THE BRUSSELATOR REACTION DIFFUSION MODEL[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(5): 541-546.
[6]	张鸿庆;闫振亚. TWO TYPES OF NEW ALGORITHMS FOR FINDING EXPLICIT ANALYTICAL SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(12): 1423-1431.
[7]	陈达段;施惟慧. ON THE FORMAL SOLUTION OF INITIAL VALUE PROBLEM OF NAVIER-STOKES EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(12): 1432-1439.
[8]	陈立群;程昌钧. DYNAMICAL BEHAVIOR OF NONLINEAR VISCOELASTIC BEAMS[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(9): 995-1001.
[9]	唐一鸣. ON THE STABILITY OF GENERAL NAVIER-STOKES TYPE EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(8): 888-894.

A FAMILY OF INTEGRABLE SYSTEMS OF LIOUVILLE AND LAX REPRESENTATION, DARBOUX TRANSFORMATIONS FOR ITS CONSTRAINED FLOWS

A FAMILY OF INTEGRABLE SYSTEMS OF LIOUVILLE AND LAX REPRESENTATION, DARBOUX TRANSFORMATIONS FOR ITS CONSTRAINED FLOWS

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 9

编辑推荐

Metrics

本文评价