A novel noncommutative KdV-type equation, its recursion operator, and solitons

被引：10

作者：

Carillo, Sandra ^{[1
,2
]}

Lo Schiavo, Mauro ^{[1
]}

Porten, Egmont ^{[3
,4
]}

Schiebold, Cornelia ^{[3
,4
]}

机构：

[1] Sapienza Univ Roma, Dipartimento SBAI, Rome, Italy

[2] INFN, Sez Roma 1, Gr Math Methods NonLinear Phys 4, Rome, Italy

[3] Mid Sweden Univ, MOD, Sundsvall, Sweden

[4] Uniwersytet Jana Kochanowskiego Kielcach, Inst Matemat, Kielce, Poland

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2018年 / 59卷 / 04期

关键词：

MATRIX GENERALIZATION; EVOLUTION-EQUATIONS;

D O I：

10.1063/1.5027481

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A noncommutative KdV-type equation is introduced extending the Backlund chart in Carillo et al. [Symmetry Integrability Geom.: Methods Appl. 12, 087 (2016)]. This equation, called meta-mKdV here, is linked by Cole-Hopf transformations to the two noncommutative versions of the mKdV equations listed in Olver and Sokolov [Commun. Math. Phys. 193, 245 (1998), Theorem 3.6]. For this meta-mKdV, and its mirror counterpart, recursion operators, hierarchies, and an explicit solution class are derived. Published by AIP Publishing.

引用

页数：14

共 50 条

[31] Exact solutions and multi-symplectic structure of the generalized KdV-type equation
Xiao-Feng Yang
Zi-Chen Deng
Qing-Jun Li
Yi Wei
Advances in Difference Equations, 2015
[32] FACTORIZATION OF THE 2X2 MATRIX RECURSION OPERATOR OF THE COUPLED KDV EQUATION
AIYER, RN
JOURNAL OF MATHEMATICAL PHYSICS, 1984, 25 (11) : 3227 - 3230
[33] Z3-SYMMETRIC CONFORMAL ALGEBRA FROM KDV-TYPE EQUATION
PARK, SU
CHO, BH
MYUNG, YS
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1988, 21 (05): : 1167 - 1171
[34] Exact solutions and multi-symplectic structure of the generalized KdV-type equation
Yang, Xiao-Feng
Deng, Zi-Chen
Li, Qing-Jun
Wei, Yi
ADVANCES IN DIFFERENCE EQUATIONS, 2015,
[35] Exact three-wave solution for higher dimensional KdV-type equation
Wang, Chuanjian
Dai, Zhengde
Liang, Lin
APPLIED MATHEMATICS AND COMPUTATION, 2010, 216 (02) : 501 - 505
[36] The geophysical KdV equation: its solitons, complexiton, and conservation laws
K. Hosseini
A. Akbulut
D. Baleanu
S. Salahshour
M. Mirzazadeh
L. Akinyemi
GEM - International Journal on Geomathematics, 2022, 13
[37] The geophysical KdV equation: its solitons, complexiton, and conservation laws
Hosseini, K.
Akbulut, A.
Baleanu, D.
Salahshour, S.
Mirzazadeh, M.
Akinyemi, L.
GEM-INTERNATIONAL JOURNAL ON GEOMATHEMATICS, 2022, 13 (01)
[38] Dromion-like structures in a (3+1)-dimensional KdV-type equation
Lou, SY
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1996, 29 (18): : 5989 - 6001
[39] An efficient algorithm of logarithmic transformation to Hirota bilinear form of KdV-type bilinear equation
Ye, Yichao
Wang, Lihong
Chang, Zhaowei
He, Jingsong
APPLIED MATHEMATICS AND COMPUTATION, 2011, 218 (05) : 2200 - 2209
[40] The noncommutative KdV equation and its para-Khler structure
DING Qing
HE ZhiZhou
ScienceChina(Mathematics), 2014, 57 (07) : 1505 - 1516

← 1 2 3 4 5 →