Higher-order solutions of a matrix AKNS system associated with a Hermitian symmetric space

2019 ◽  
Vol 383 (25) ◽  
pp. 3047-3055 ◽  
Author(s):  
Xianguo Geng ◽  
Jing Shen ◽  
Bo Xue
Keyword(s):  
Symmetric Space ◽  
Higher Order ◽  
Hermitian Symmetric Space ◽  
Akns System

scholarly journals Integrable systems with unitary invariance from non-stretching geometric curve flows in the Hermitian symmetric space Sp(n)/U(n)

2015 ◽  
Vol 38 ◽  
pp. 1560071 ◽  
Author(s):  
Stephen C. Anco ◽  
Esmaeel Asadi ◽  
Asieh Dogonchi
Keyword(s):  
Symmetric Space ◽  
Integrable Systems ◽  
Hermitian Symmetric Space ◽  
Complex Matrix ◽  
Curve Flows ◽  
Frame Method ◽  
Parallel Frame ◽  
Natural Way ◽  
Sg Equation ◽  
Unitary Invariance

A moving parallel frame method is applied to geometric non-stretching curve flows in the Hermitian symmetric space Sp(n)/U(n) to derive new integrable systems with unitary invariance. These systems consist of a bi-Hamiltonian modified Korteweg-de Vries equation and a Hamiltonian sine-Gordon (SG) equation, involving a scalar variable coupled to a complex vector variable. The Hermitian structure of the symmetric space Sp(n)/U(n) is used in a natural way from the beginning in formulating a complex matrix representation of the tangent space 𝔰𝔭(n)/𝔲(n) and its bracket relations within the symmetric Lie algebra (𝔲(n), 𝔰𝔭(n)).

scholarly journals Hermitian symmetric space, flat bundle and holomorphicity criterion

2016 ◽  
Vol 140 (4) ◽  
pp. 1-10
Author(s):  
Hassan Azad ◽  
Indranil Biswas ◽  
C.S. Rajan ◽  
Shehryar Sikander
Keyword(s):  
Symmetric Space ◽  
Hermitian Symmetric Space ◽  
Flat Bundle

scholarly journals Zero Curvature Formalism for Supersymmetric Integrable Hierarchies in Superspace

1997 ◽  
Vol 12 (34) ◽  
pp. 2623-2630 ◽  
Author(s):  
H. Aratyn ◽  
C. Rasinariu ◽  
A. Das
Keyword(s):  
Symmetric Space ◽  
Integrable Systems ◽  
Integrable Hierarchies ◽  
Space Structure ◽  
Hermitian Symmetric Space ◽  
Curvature Condition ◽  
Lax Equation ◽  
Abelian Gauge ◽  
Graded Algebras ◽  
Zero Curvature

We generalize the Drinfeld–Sokolov formalism of bosonic integrable hierarchies to superspace, in a way which systematically leads to the zero curvature formulation for the supersymmetric integrable systems starting from the Lax equation in superspace. We use the method of symmetric space as well as the non-Abelian gauge technique to obtain the supersymmetric integrable hierarchies of the AKNS type from the zero curvature condition in superspace with the graded algebras, sl (n+1,n), providing the Hermitian symmetric space structure.

scholarly journals Colliding scalar pulses in the Einstein-Gauss-Bonnet gravity

2018 ◽  
Vol 168 ◽  
pp. 04014
Author(s):  
Hisaaki Shinkai ◽  
Takashi Torii
Keyword(s):  
Nonlinear Dynamics ◽  
Symmetric Space ◽  
Higher Order ◽  
Space Time ◽  
Large Curvature ◽  
Bonnet Gravity ◽  
Plane Symmetric ◽  
Higher Order Curvature Corrections

We numerically investigated how the nonlinear dynamics depends on the dimensionality and on the higher-order curvature corrections in the form of Gauss-Bonnet (GB) terms, with a model of colliding scalar pulses in plane-symmetric space-time. We observed that a collision of large scalar pulses will produce a large-curvature region, of which the magnitude depends on αGB. The normal corrections (αGB > 0) work for avoiding the appearance of singularity, although it is inevitable.

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