Multi-linear variable separation approach to nonlinear systems

被引：16

作者：

Tang, Xiao-yan ^{[1
]}

Lou, Sen-yue ^{[1
,2
,3
]}

机构：

[1] Shanghai Jiao Tong Univ, Dept Phys, Shanghai 200240, Peoples R China

[2] Ningbo Univ, Dept Phys, Ningbo 315211, Zhejiang, Peoples R China

[3] Fudan Univ, Sch Math, Shanghai 200433, Peoples R China

来源：

FRONTIERS OF PHYSICS IN CHINA | 2009年 / 4卷 / 02期

基金：

中国国家自然科学基金;

关键词：

multi-linear variable separation approach (MLVSA); multi-linear variable separation solution (MLVSS); universal formula; SCHRODINGER-EQUATION; EXCITATIONS; FRACTALS; SOLITONS; CHAOS;

D O I：

10.1007/s11467-009-0046-2

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The multi-linear variable separation approach is reviewed in this article. The method has been recently established and successfully solved a large number of nonlinear systems. One of the most exciting findings is that the basic multi-linear variable separation solution can be expressed by a universal formula including two (1+1)-dimensional functions, and at least one is arbitrary for integrable systems. Furthermore, the method has been extended in two different ways so as to enroll more low dimensional functions in the solution.

引用

页码：235 / 240

页数：6

共 50 条

[1] Multi-linear variable separation approach to nonlinear systems
Xiao-yan Tang
Sen-yue Lou
[J]. Frontiers of Physics in China, 2009, 4 : 235 - 240
[2] Notes on multi-linear variable separation approach
Shen, SF
Zhang, J
Pan, ZL
[J]. COMMUNICATIONS IN THEORETICAL PHYSICS, 2005, 43 (04) : 582 - 584
[3] Notes on Multi-linear Variable Separation Approach
SHEN Shou-Feng
ZHANG Jun
PAN Zu-Liang Department of Mathematics
[J]. Communications in Theoretical Physics, 2005, 43 (04) : 582 - 584
[4] General multi-linear variable separation approach to solving low dimensional nonlinear systems and localized exitations
Shen, SF
[J]. ACTA PHYSICA SINICA, 2006, 55 (03) : 1011 - 1015
[5] Multi-linear variable separation approach to solve a (2+1)-dimensional generalization of nonlinear Schrodinger system
Shen, SF
Zhang, J
Pan, ZL
[J]. COMMUNICATIONS IN THEORETICAL PHYSICS, 2005, 43 (06) : 965 - 968
[6] Multi-linear Variable Separation Approach to Solve a (2+1)-Dimensional Generalization of Nonlinear Schrodinger System
SHEN Shou-Feng
ZHANG Jun
PAN Zu-Liang Department of Mathematics
[J]. Communications in Theoretical Physics, 2005, 43 (06) : 965 - 968
[7] A nonlinear control design approach based on multi-linear models
Palizban, HA
Safavi, AA
Romagnoli, JA
[J]. PROCEEDINGS OF THE 1997 AMERICAN CONTROL CONFERENCE, VOLS 1-6, 1997, : 3490 - 3494
[8] Multi-linear Variable Separation Approach to Solve a(1+1)-Dimensional Coupled Integrable Dispersionless System
SHEN Shou-Feng Department of Mathematics
[J]. Communications in Theoretical Physics, 2005, 44 (11) : 779 - 782
[9] Multi-linear variable separation approach to solve a (1+1)-dimensional coupled integrable dispersionless system
Shen, SF
[J]. COMMUNICATIONS IN THEORETICAL PHYSICS, 2005, 44 (05) : 779 - 782
[10] Variable Separation Approach to Solve Nonlinear Systems
SHEN Shou-Feng~1 PAN Zu-Liang~1 ZHANG Jun~21 Department of Mathematics
[J]. Communications in Theoretical Physics, 2004, 42 (10) : 565 - 567

← 1 2 3 4 5 →