Related papers: Transverse Evolution Operator for the Gross-Pitaev…
A semiclassical approximation for an evolving density operator, driven by a "closed" hamiltonian operator and "open" markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the…
Weakly nonlinear analysis of resonant PDEs in recent literature has generated a number of resonant systems for slow evolution of the normal mode amplitudes that possess remarkable properties. Despite being infinite-dimensional Hamiltonian…
We present a new method to solve in a semianalytical way the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NLO order in the x-space. The method allows to construct an evolution operator expressed in form of a rapidly…
We study the asymptotic behavior of the trajectory of a nonautonomous evolution equation governed by a quasi-nonexpansive operator in Hilbert spaces. We prove the weak convergence of the trajectory to a fixed point of the operator by…
In this paper the semi-classical approach to the solution of non-linear evolution equation is developed. We found the solution in the entire kinematic region to the non-linear evolution equation that governs the dynamics in the high parton…
We deal with the $n$-dimensional nonlinear Schr\"{o}dinger equation (NLSE) with a cubic nonlocal nonlinearity and an anti-Hermitian term, which is widely used model for the study of open quantum system. We construct asymptotic solutions to…
We consider semiclassically scaled, weakly nonlinear Schr\"odinger equations with external confining potentials and additional angular-momentum rotation term. This type of model arises in the Gross-Pitaevskii theory of trapped, rotating…
We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is…
We present a local framework for investigating non-unitary evolution groups pertinent to effective field theories in general semi-classical spacetimes. Our approach is based on a rigorous local stability analysis of the algebra of…
We develop numerical methods for solving the spin-2 Gross-Pitaevskii equation. The basis of our work is a two-way splitting of this evolution equation that leads to two exactly solvable subsystems. Utilizing second-order and fourth-order…
In this paper we consider fully discrete approximations of abstract evolution equations, by means of a quasi non-conforming spatial approximation and finite differences in time (Rothe-Galerkin method). The main result is the convergence of…
We develop generalized Petersson/Bruggeman-Kuznetsov (PBK) formulas for specified local components at non-archimedean places. In fact, we introduce two hypotheses on non-archimedean test function pairs $f \leftrightarrow \pi(f)$, called…
In this work we study symplectic unitary representations for the Galilei group. As a consequence a Non-Linear Schr\"odinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and…
We study generalized solutions of an evolutionary equation related to a densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and find…
We consider the applications of a numerical-analytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of Vlasov-Poisson/Maxwell equations. We calculate the…
A microscopic theory of linear response based on the Vlasov equation is extended to systems having spheroidal equilibrium shape. The solution of the linearized Vlasov equation, which gives a semiclassical version of the random phase…
The present work is concerned with the extension of modified potential operator splitting methods to specific classes of nonlinear evolution equations. The considered partial differential equations of Schr{\"o}dinger and parabolic type…
We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational…
This contribution is dedicated to the exploration of exponential operator splitting methods for the time integration of evolution equations. It entails the review of previous achievements as well as the depiction of novel results. The…
The conformal mapping approach is a well established technique for solving the Euler equations for potential flows with one spatial dimension. In this work, we extend this framework to problems with a weakly transversal dependence and, by…