Darboux integrable discrete equations possessing an autonomous first-order integral
نویسندگان
چکیده
منابع مشابه
Darboux-integrable equations with non-Abelian nonlinearities
We introduce a new class of nonlinear equations admitting a representation in terms of Darboux-covariant compatibility conditions. Their special cases are, in particular, (i) the “general” von Neumann equation iρ̇ = [H, f(ρ)], with [f(ρ), ρ] = 0, (ii) its generalization involving certain functions f(ρ) which are non-Abelian in the sense that [f(ρ), ρ] 6= 0, and (iii) the Nahm equations.
متن کاملPartial differential equations possessing Frobenius integrable decompositions
Frobenius integrable decompositions are introduced for partial differential equations. A procedure is provided for determining a class of partial differential equations of polynomial type, which possess specified Frobenius integrable decompositions. Two concrete examples with logarithmic derivative Bäcklund transformations are given, and the presented partial differential equations are transfor...
متن کاملDarboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation
The paper presents two results. First it is shown how the discrete potential modified KdV equation and its Lax pairs in matrix form arise from the Hirota–Miwa equation by a 2-periodic reduction. Then Darboux transformations and binary Darboux transformations are derived for the discrete potential modified KdV equation and it is shown how these may be used to construct exact solutions.
متن کاملContinuous-discrete integrable equations and Darboux transformations as deformations of associative algebras
Deformations of the structure constants for a class of associative noncommutative algebras generated by Deformation Driving Algebras (DDA’s) are defined and studied. These deformations are governed by the Central System (CS). Such a CS is studied for the case of DDA being the algebra of shifts. Concrete examples of deformations for the three-dimensional algebra governed by discrete and mixed co...
متن کاملMulticomponent integrable wave equations: I. Darboux-dressing transformation
The Darboux-dressing transformations are applied to the Lax pair associated with systems of coupled nonlinear wave equations in the case of boundary values which are appropriate to both ‘bright’ and ‘dark’ soliton solutions. The general formalism is set up and the relevant equations are explicitly solved. Several instances of multicomponent wave equations of applicative interest, such as vector...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2014
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/47/10/105204