Results 251 to 260 of about 2,529,460 (286)

Zero Curvature Formulations of Dual Hierarchies

Journal of Mathematical Physics, 1996
Zero curvature formulations are given for the “dual hierarchies ” of stan-dard soliton equation hierarchies, recently introduced by Olver and Rosenau, including the physically interesting Fuchssteiner-Fokas-Camassa-Holm hierarchy. PACS Numbers: 03.40.Kf,
Jeremy Schiff
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Complex Structures and Zero-Curvature Equations for σ-Models

Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 2016
We construct zero-curvature representations for the equations of motion of a class of sigma-models with complex homogeneous target spaces, not necessarily symmetric. We show that in the symmetric case the proposed flat connection is gauge-equivalent to the conventional one.
Dmitri Bykov
exaly   +5 more sources

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The Zero Curvature Formulation of the sKdV Equations

Journal of Mathematical Physics, 1990
The fermionic extensions of the KdV equation are derived from the zero curvature condition associated with the superalgebra OSp(2‖1). This derivation clarifies why there are only two such extensions possible and why only one of them is supersymmetric. A Lenard type of derivation of these equations is also presented.
Shibaji Roy, Ashok Das
exaly   +2 more sources

The Zero Curvature Formulation of the KP and the sKP Equations

Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 1992
Abstract The Kadomtsev-Petviashvili equation is derived from the zero curvature condition associated with the gauge group SL (2, R ) in 2 + 1 dimensions. A fermionic extension of the KP equation is also obtained using the zero curvature condition of the supergroup OSp(2∥1), which reduces upon appropriate restriction to the Kupershmidt equation.
Shibaji Roy, Ashok Das, Sudhakar Panda
exaly   +2 more sources

Hamiltonians and zero-curvature equations for integrable partial differential equations

Journal of Mathematical Physics, 2001
We discuss the relationship between two approaches to integrable partial differential equations, one using formal affine Lie algebras and the other Banach–Lie groups. In the first approach integrability of the equations follows from commutativity of Hamiltonian flows on the Lie algebra, while in the second it follows from commutativity of certain flows
Adams, Malcolm R., Krešić-Jurić, Saša   +1 more
openaire   +4 more sources

Fractional Zero Curvature Equation and Generalized Hamiltonian Structure of Soliton Equation Hierarchy

International Journal of Theoretical Physics, 2007
The authors of this interesting paper consider the fractional zero curvature equation of the form \[ {\mathbf D}_t^{\alpha}U-{\mathbf D}_x^{\alpha}V + [U,V] = 0, \] where \({\mathbf D}_t^{\alpha}(f(t))\) is the fractional derivative introduced by \textit{H. D. Davis} [Monogr. of the Qaterman Inst. of Indiana Univ.
Hong-Qing Zhang, Yu Fa-Jun
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Constructing (2+1)-Dimensional Nonlinear Soliton Equations With a Generalized Zero Curvature Equation

Applied Mathematics and Computation, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fajun yu
exaly   +4 more sources

The Zero Curvature Formulation of the Boussinesq Equation

Physics Letters, Section A: General, Atomic and Solid State Physics, 1991
Abstract We derive the Boussineq equation from the zero curvature condition associated with the group SL (3, R ). We also present a connection between this formulation and the one based on a combined conformal and spin-3 flow.
Shibaji Roy, Ashok Das, Wen-Jui Huang
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The Zero Curvature Representation for Hierarchies of Nonlinear Evolution Equations

Physics Letters, Section A: General, Atomic and Solid State Physics, 2000
Abstract Directly starting from the spectral problem ψ x = U ( u , λ ) ψ and with help of functional gradient, a simple method is proposed for constructing zero curvature representation of the hierarchies of nonlinear evolution equations.
Engui Fan
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Algebraic Structure of Discrete Zero Curvature Equations and Master Symmetries of Discrete Evolution Equations [PDF]

Journal of Mathematical Physics, 1999
An algebraic structure related to discrete zero curvature equations is established. It is used to give an approach for generating master symmetries of the first degree for systems of discrete evolution equations and an answer to why there exist such master symmetries.
Wen-Xiu Ma, Benno Fuchssteiner
exaly   +4 more sources