Darboux Integrable System with a Triple Point and Pseudo-Abelian Integrals
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 کاملAn extended complete Chebyshev system of 3 Abelian integrals related to a non-algebraic Hamiltonian system
In this paper, we study the Chebyshev property of the 3-dimentional vector space $E =langle I_0, I_1, I_2rangle$, where $I_k(h)=int_{H=h}x^ky,dx$ and $H(x,y)=frac{1}{2}y^2+frac{1}{2}(e^{-2x}+1)-e^{-x}$ is a non-algebraic Hamiltonian function. Our main result asserts that $E$ is an extended complete Chebyshev space for $hin(0,frac{1}{2})$. To this end, we use the criterion and tools developed by...
متن کاملDarboux Transformations for a Lax Integrable System in 2n-Dimensions
A 2n-dimensional Lax integrable system is proposed by a set of specific spectral problems. It contains Takasaki equations, the self-dual Yang-Mills equations and its integrable hierarchy as examples. An explicit formulation of Darboux transformations is established for this Lax integrable system. The Vandermonde and generalized Cauchy determinant formulas lead to a description for deriving expl...
متن کاملRedundant Picard–fuchs System for Abelian Integrals
We derive an explicit system of Picard–Fuchs differential equations satisfied by Abelian integrals of monomial forms and majorize its coefficients. A peculiar feature of this construction is that the system admitting such explicit majorants, appears only in dimension approximately two times greater than the standard Picard–Fuchs system. The result is used to obtain a partial solution to the tan...
متن کاملDarboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations
In this paper we study the Darboux transformations of planar vector fields of Schrödinger type. Using the isogaloisian property of Darboux transformation we prove the “invariance” of the objects of the “Darboux theory of integrability”. In particular, we also show how the shape invariance property of the potential is important in order to preserve the structure of the transformed vector field. ...
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 Dynamical and Control Systems
سال: 2020
ISSN: 1079-2724,1573-8698
DOI: 10.1007/s10883-020-09477-3