We establish a formal variational calculus of supervariables, which is a combination of the bosonic theory of Gel’fand-Dikii and the fermionic theory in our earlier work. Certain interesting new algebraic structures are found in connection with Hamiltonian superoperators in terms of our theory. In particular, we find connections between Hamiltonian superoperators and NovikovPoisson algebras tha...

Abstract In this work, we give a quantitative answer to the question: how sudden or adiabatic is frequency change in quantum harmonic oscillator (HO)? We do that by studying time evolution of HO which initially its fundamental state and whose time-dependent controlled parameter (denoted ϵ ) can continuously tune from totally slow process completely abrupt one. extend solution based on algebraic...

This is a review of two of the fundamental tools for analysis of soliton equations: i) the algebraic ones based on Kac-Moody algebras, their central extensions and their dual algebras which underlie the Hamiltonian structures of the NLEE; ii) the construction of the fundamental analytic solutions (FAS) of the Lax operator and the Riemann-Hilbert problem (RHP) which they satisfy. The fact that t...

In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...

A study of symplectic forms associated with two dimensional quantum planes and the quantum sphere in a three dimensional orthogonal quantum plane is provided. The associated Hamiltonian vector fields and Poissonian algebraic relations are made explicit.

A symplectic theory approach is devised for solving the problem of algebraic-analytical construction of integral submanifold imbeddings for integrable (via the nonabelian Liouville-Arnold theorem) Hamiltonian systems on canonically symplectic phase spaces.

The problem of the Hamiltonian matrix in the oscillator and orthogonalized Laguerre basis construction from a given S-matrix is treated in the context of the algebraic analogue of the Marchenko method.

There is proposed a symplectic theory approach to studying integrable via the nonabelian Liouville-Arnold theorem Hamiltonian systems on canonically symplectic phase spaces. A method of algebraic-analytical constructing the corresponding integral submanifold imbedding mappings is devised.

A Hamiltonian system in potential form (H(q, p) = p'M~ 'p/2 + E(q)) subject to smooth constraints on q can be viewed as a Hamiltonian system on a manifold, but numerical computations must be performed in R" . In this paper, methods which reduce "Hamiltonian differential-algebraic equations" to ODEs in Euclidean space are examined. The authors study the construction of canonical parametrizations...