Related papers: Integrated Lax Formalism for PCM
The path integral formulation of singular systems with second order Lagrangian is studied by using the canonical path integral method. The path integral of Podolsky electrodynamics is studied.
We equip the whole space of fields of the triplectic formalism of Lagrangian quantization with an even supersymplectic structure and clarify its geometric meaning. We also discuss its relation to a closed two-form arising naturally in the…
This paper is the second in a series of works dedicated to studying non-linear partial differential equations via derived geometric methods. We study a natural derived enhancement of the de Rham complex of a non-linear PDE via…
Variational integrators applied to degenerate Lagrangians that are linear in the velocities are two-step methods. The system of modified equations for a two-step method consists of the principal modified equation and one additional equation…
We formalize the Gauss-Landau theorem, providing a unified prime factorization approach to computing the GCD and LCM of finite nonzero integer sets. Although commonly used as a heuristic or technique in elementary number theory education,…
By applying the perturbation function approach, we propose the Lagrangian and the conjugate duals for minimization problems of the sum of two, generally nonconvex, functions. The main tools are the $\Phi$-convexity theory and minimax…
We introduce a class of integrable $l$-field first-order lattices together with corresponding Lax equations. These lattices may be represented as consistency condition for auxiliary linear systems defined on sequences of formal dressing…
For propagation of surface shallow-water waves on irrotational flows, we derive a new two-component system. The system is obtained by a variational approach in the Lagrangian formalism. The system has a non-canonical Hamiltonian…
The integrable 1+1-dimensional SU(2) principal chiral model (PCM) serves as a toy-model for 3+1-dimensional Yang-Mills theory as it is asymptotically free and displays a mass gap. Interestingly, the PCM is 'pseudodual' to a scalar field…
The relation between integrable systems and algebraic geometry is known since the XIXth century. The modern approach is to represent an integrable system as a Lax equation with spectral parameter. In this approach, the integrals of the…
Field theoretical models with first order Lagrangean can be formulated in a covariant Hamiltonian formalism. In this article, the geometrical construction of the Gerstenhaber structure that encodes the equations of motion is explained for…
Appropriate restrictions of Lax operators which allows to construction of (2+1)-dimensional integrable field systems, coming from centrally extended algebra of pseudo-differential operators, are reviewed. The gauge transformation and the…
In this article, we discuss formal invariants of singularly-perturbed linear differential systems in neighborhood of turning points and give algorithms which allow their computation. The algorithms proposed are implemented in the computer…
We present the symplectic algorithm in the Lagrangian formalism for the Hamiltonian systems by virtue of the noncommutative differential calculus with respect to the discrete time and the Euler--Lagrange cohomological concepts. We also show…
We present a general procedure to solve the equations of motion for cosmological models driven by real scalar fields with first-order differential equations. The method seems to have great power, since it works for closed, flat or open…
A Lagrangian multiform structure is established for a generalisation of the Darboux system describing orthogonal curvilinear coordinate systems. It has been shown in the past that this system of coupled PDEs is in fact an encoding of the…
This is the first installment of an exposition of an ACL2 formalization of elementary linear algebra, focusing on aspects of the subject that apply to matrices over an arbitrary commutative ring with identity, in anticipation of a future…
We study static kink configurations in a type of two-dimensional higher derivative scalar field theory whose Lagrangian contains second-order derivative terms of the field. The linear fluctuation around arbitrary static kink solutions is…
We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…
This work is devoted to review the gauge embedding of either commutative and noncommutative (NC) theories using the symplectic formalism framework. To sum up the main features of the method, during the process of embedding, the…