Results 31 to 40 of about 6,081 (189)
Differential Calculi on Associative Algebras and Integrable Systems
, 2020 After an introduction to some aspects of bidifferential calculus on associative algebras, we focus on the notion of a "symmetry" of a generalized zero curvature equation and derive Backlund and (forward, backward and binary) Darboux transformations from ...
A Dimakis +30 more
core +1 more source
On the Relationship between Two Notions of Compatibility for Bi-Hamiltonian Systems [PDF]
, 2015 Bi-Hamiltonian structures are of great importance in the theory of integrable Hamiltonian systems. The notion of compatibility of symplectic structures is a key aspect of bi-Hamiltonian systems.
Santoprete, Manuele
core +4 more sources
Darboux-Integrability and Uniform Convergence
Real Analysis Exchange, 2004 A concept of Darboux-integrability for Banach space-valued functions defined on a basic space \((\Omega, {\mathcal D}, \mu)\) is introduced. In the finite-dimensional case for functions on \([a,b]\) this concept generalizes the Riemann integral, but in the infinite-dimensional case the Darboux-integral is more restrictive than the standard definition ...
openaire +3 more sources
Advances in Mathematical Physics, 2014 We derive the solitonic solution of the nonlinear Schrödinger equation with cubic nonlinearity, complex potentials, and time-dependent coefficients using the Darboux transformation.
H. Chachou Samet +3 more
doaj +1 more source
Finiteness of integrable $n$-dimensional homogeneous polynomial potentials
, 2007 We consider natural Hamiltonian systems of $n>1$ degrees of freedom with polynomial homogeneous potentials of degree $k$. We show that under a genericity assumption, for a fixed $k$, at most only a finite number of such systems is integrable.
Ablowitz +32 more
core +2 more sources
On integrability aspects of the supersymmetric sine-Gordon equation
, 2017 In this paper we study certain integrability properties of the supersymmetric sine-Gordon equation. We construct Lax pairs with their zero-curvature representations which are equivalent to the supersymmetric sine-Gordon equation.
Bertrand, Sébastien
core +1 more source
Integrable discrete nets in Grassmannians
, 2008 We consider discrete nets in Grassmannians $\mathbb{G}^d_r$ which generalize Q-nets (maps $\mathbb{Z}^N\to\mathbb{P}^d$ with planar elementary quadrilaterals) and Darboux nets ($\mathbb{P}^d$-valued maps defined on the edges of $\mathbb{Z}^N$ such that ...
A. Doliwa +10 more
core +1 more source
The role of algebraic solutions in planar polynomial differential systems [PDF]
, 2005 We study a planar polynomial differential system, given by \dot{x}=P(x,y), \dot{y}=Q(x,y). We consider a function I(x,y)=\exp \{h_2(x) A_1(x,y) \diagup A_0(x,y) \} h_1(x) \prod_{i=1}^{\ell} (y-g_i(x))^{\alpha_i}, where g_i(x) are algebraic functions, A_1(
Giacomini, Héctor +2 more
core +5 more sources
Inverse Problems in Darboux’ Theory of Integrability [PDF]
Acta Applicandae Mathematicae, 2012 The Darboux theory of integrability for planar polynomial differential equations is a classical field, with connections to Lie symmetries, differential algebra and other areas of mathematics. In the present paper we introduce the concepts, problems and inverse problems, and we outline some recent results on inverse problems. We also prove a new result,
Christopher, Colin +3 more
openaire +5 more sources
C∞‐Structures for Liénard Equations and New Exact Solutions to a Class of Klein–Gordon Equations
Mathematical Methods in the Applied Sciences, Volume 49, Issue 4, Page 2795-2822, 15 March 2026.ABSTRACT Liénard equations are analyzed using the recent theory of 𝒞∞‐structures. For each Liénard equation, a 𝒞∞‐structure is determined by using a Lie point symmetry and a 𝒞∞‐symmetry. Based on this approach, a novel method for integrating these equations is proposed, which consists in solving sequentially two completely integrable Pfaffian equations.
Beltrán de la Flor +2 more
wiley +1 more source