Results 11 to 20 of about 2,529,460 (286)
British Journal of Applied Science & Technology, 2013 Binary operations are introduced for triples satisfying zero curvature equations and quadruples satisfying generalized zero curvature equations, and it is shown that such operations define Lie algebra structures on the corresponding spaces of triples and quadruples.
Wen-Xiu Ma
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Soliton equations and the zero curvature condition in noncommutative geometry [PDF]
Journal of Physics A: Mathematical and General, 1996 Familiar nonlinear and in particular soliton equations arise as zero curvature conditions for GL(1,R) connections with noncommutative differential calculi. The Burgers equation is formulated in this way and the Cole-Hopf transformation for it attains the interpretation of a transformation of the connection to a pure gauge in this mathematical framework.
Dimakis, Aristophanes +1 more
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A Note on Lax Pairs of the Sawada-Kotera Equation [PDF]
Journal of Mathematics, 2014 We prove that the new Lax pair of the Sawada-Kotera equation, discovered recently by Hickman, Hereman, Larue, and Göktaş, and the well-known old Lax pair of this equation, considered in the form of zero-curvature representations, are gauge equivalent to ...
Sergei Sakovich
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On Construction of a Super Hierarchy of the Wadati-Konno-Ichikawa Equation
Advances in Mathematical Physics, 2020 In this paper, a super Wadati-Konno-Ichikawa (WKI) hierarchy associated with a 3×3 matrix spectral problem is derived with the help of the zero-curvature equation.
Xuemei Li, Lutong Li
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Contact Integrable Extensions and Zero-Curvature Representations for the Second Heavenly Equation
, 2011 The method of contact integrable extensions is used to find new zero-curvature representation for Plebañski's second heavenly equation.
Oleg I. Morozov
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Reducibility of zero curvature equations
Electronic Journal of Differential Equations, 2004 A pair \(( \Theta _{1},\Theta _{2}) \) of smooth complex \(n\times n\)-matrix functions in the variables \(( s,t) \in \mathbb{R}^{2}\) is called a compatible pair if there exists a smooth complex function \(G( s,t) \) satisfying \[ \frac{\partial G}{\partial s}=\Theta _{1}G, \quad \frac{\partial G}{\partial t}=\Theta _{2}G, \] with the initial ...
Flores-Espinoza, Ruben
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On zero-curvature representations of evolution equations [PDF]
Journal of Physics A: Mathematical and General, 1995 Zero-curvature representations (ZCRs) \[ D_t A- D_x B-[A,B ]=0 \] of evolution equations \(u_t= f(x, u, u_1, \dots, u_n)\) are investigated in this paper. It is shown that the existence condition of the ZCR with matrices \(A= A(x, u, u_1, \dots, u_i)\) and \(B= B(x, u, u_1, \dots,u_{i+n -1})\) can be represented in the form \[ fC= \nabla P, \] where ...
Gianni Manno, Sergei Igonin
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Subharmonic solutions of the prescribed curvature equation [PDF]
, 2015 We study the existence of subharmonic solutions of the prescribed curvature equation . According to the behavior at zero, or at infinity, of the prescribed curvature f, we prove the existence of arbitrarily small classical subharmonic solutions, or ...
Chiara Corsato +5 more
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LARGE SOLUTIONS FOR YAMABE AND SIMILAR PROBLEMS ON DOMAINS IN RIEMANNIAN MANIFOLDS [PDF]
, 2011 We present a unified approach to study large positive solutions (i.e., u(x) -> infinity as x -> partial derivative Omega) of the equation Delta u + hu - k psi(u) = -f in an arbitrary domain Omega.
Martin Dindoš, Dindos, Martin; id_orcid
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Soliton Equations Extracted from the Noncommutative Zero-Curvature Equation [PDF]
Progress of Theoretical Physics, 2001 We investigate the equation where the commutation relation in 2-dimensional zero-curvature equation composed of the algebra-valued potentials is replaced by the Moyal bracket and the algebra-valued potentials are replaced by the non-algebra-valued ones with two more new variables.
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