相关论文: Continuous changes of variables and the Magnus exp…
Magnus expansion is used to identify effective Hamiltonians describing the coarse-grained dynamics of more complex problems. Here, we apply this method to a two-level system driven by an and AC field. We derive Stark and Bloch-Siegert shifs…
In this article we present the first results on domain decomposition methods for nonlocal operators. We present a nonlocal variational formulation for these operators and establish the well-posedness of associated boundary value problems,…
We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional…
We study Schr\"odinger operators with Floquet boundary conditions on flat tori obtaining a spectral result giving an asymptotic expansion of all the eigenvalues. The expansion is in $\lambda^{-\delta}$ with $\delta\in(0,1)$ for most of the…
We present an elementary approach to observe frequency cascade on forced nonlinear Schr{\"o}dinger equations. The forcing term (which may also appear as a potential term instead) consists of a constant term, perturbed by a modulated…
We exhibit a method to numerically compute power series expansions of modular forms on a cocompact Fuchsian group, using the explicit computation a fundamental domain and linear algebra.
We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric…
We give fully explicit upper and lower bounds for the constants in two known inequalities related to the quadratic nonlinearity of the incompressible (Euler or) Navier-Stokes equations on the torus T^d. These inequalities are "tame"…
We are concerned with a class of nonlinear Schr\"{o}dinger-type equations with a reaction term and a differential operator that involves a variable exponent. By using related variational methods, we establish several existence results.
Anomalous dynamics characterized by non-Gaussian probability distributions (PDFs) and/or temporal long-range correlations can cause subtle modifications of conventional fluctuation relations. As prototypes we study three variants of a…
In a previous study, the algebraic formulation of the First Fundamental Theorem of Calculus (FFTC) is shown to allow extensions of differential and Rota-Baxter operators on the one hand, and to give rise to categorical explanations using…
The unitary operators U(t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-dependent invariants. We clarify the role of Lie-algebraic…
Selfdual variational calculus is further refined and used to address questions of existence of local and global solutions for various parabolic semi-linear equations, Hamiltonian systems of PDEs, as well as certain nonlinear Schrodinger…
The Darboux transformation (DT) formulae for the derivative nonlinear Schr\"{o}dinger (DNLS) equation are expressed in concise forms, from which the multi-solitons, n-periodic solutions, higher-order hybrid-pattern solitons and some mixed…
In this paper, the Talbot effect for the multi-component linear and nonlinear systems of the dispersive evolution equations on a bounded interval subject to periodic boundary conditions and discontinuous initial profiles is investigated.…
Asymptotic expansion of a variation with anticipative weights is derived by the theory of asymptotic expansion for Skorohod integrals having a mixed normal limit. The expansion formula is expressed with the quasi-torsion, quasi-tangent and…
Deviations from kinetic equilibrium of massive particles caused by the universe expansion are calculated analytically in the Boltzmann approximation. For the case of an energy independent amplitude of elastic scattering, an exact partial…
A new method named rational expansion method of exponent function is presented to find exact traveling wave solutions of differential-difference equations. This method generalizes the so-called tanh-method and other similar methods. Some…
This article reveals a specific category of solutions for the $1+1$ Variable Order (VO) nonlinear fractional Fokker-Planck equations. These solutions are formulated using VO $q$-Gaussian functions, granting them significant versatility in…
We study higher-order small-noise fluctuation expansions for the overdamped Langevin dynamics in a quartic double-well potential. Assuming that the initial data admits a suitable expansion structure, we obtain a strong dynamical expansion…