相关论文: On the tritronqu\'ee solutions of P$_I^2$

We investigate the long-time asymptotic behavior of a class of solutions to the defocusing Manakov system under nonzero boundary conditions. These solutions are characterized by a $3 \times 3$ matrix Riemann Hilbert problem. We find that…

We establish semiclassical asymptotics and estimates for the $e_h(x,x;\tau)$ where $e_h(x,y,\tau)$ is the Schwartz kernel of the spectral projector for a second order elliptic operator inside domain with power singularity in the origin.…

We study the asymptotic behaviour of orthogonal polynomials in the complex plane that are associated to a certain normal matrix model. The model depends on a parameter and the asymptotic distribution of the eigenvalues undergoes a…

In this work we study the Plancherel-Rotach type asymptotics for selected $q$-series and $q$-orthogonal polynomials with complex scalings. The $q$-series we cover are Euler's $q$-exponential, Ramanujan function, Jackson's $q$-Bessel…

The second Stokes problem about behaviour of the rarefied gas filling half-space is formulated. A plane, limiting half-space, makes harmonious oscillations in the plane. The kinetic equation with modelling integral of collisions in the form…

We consider the Schr\"odinger equation with nonlinear dissipation \begin{equation*} i \partial _t u +\Delta u=\lambda|u|^{\alpha}u \end{equation*} in ${\mathbb R}^N $, $N\geq1$, where $\lambda\in {\mathbb C} $ with $\Im\lambda<0$. Assuming…

In the case of polynomial potentials all solutions to 1-D Schroedinger equation are entire functions totally determined by loci of their roots and their behaviour at infinity. In this paper a description of the first of the two properties…

We consider polynomials $P_n$ orthogonal with respect to the weight $J_{\nu}$ on $[0,\infty)$, where $J_{\nu}$ is the Bessel function of order $\nu$. Asheim and Huybrechs considered these polynomials in connection with complex Gaussian…

We study the planar and scalar reductions of the nonlinear Lindemann mechanism of unimolecular decay. First, we establish that the origin, a degenerate critical point, is globally asymptotically stable. Second, we prove there is a unique…

The asymptotic iteration method is used to find exact and approximate solutions of Schroedinger's equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent).…

We apply the asymptotic iteration method (AIM) [J. Phys. A: Math. Gen. 36, 11807 (2003)] to solve new classes of second-order homogeneous linear differential equation. In particular, solutions are found for a general class of eigenvalue…

We prove regularity results for solutions of the equation \[div(< AXu,X u>^{(p-2)/2} AX u) = 0,\] $1<p<\infty$, where $X=(X_1,...,X_m)$ is a family of vector fields satisfying H\"ormander's ellipticity condition, $A$ is an $m\times m$…

We propose a new method for the evaluation of intersection numbers for twisted meromorphic $n$-forms, through Stokes' theorem in $n$ dimensions. It is based on the solution of an $n$-th order partial differential equation and on the…

We show the existence and uniqueness of bounded solutions to the degenerate complex Monge-Amp\`ere type equations on compact Hermitian manifolds. We also study the asymptotics of these solutions. As applications, we give partial answers to…

Consider the two-dimensional, incompressible Navier-Stokes equations on the torus We prove that the semigroup P_t generated by the solutions to stochastic Navier-stokes equations is asymptotically strong Feller. Moreover, we also prove that…

This paper deals with the asymptotic study of the so-called canard solutions, which arise in the study of real singularly perturbed ODEs. Starting near an attracting branch of the "slow curve", those solutions are crossing a turning point…

Under this method second order \textbf{partial differential equations (PDE's)} can be reduce to first order PDE's, simplifying the Initial value problem \textbf{IVP} or Border value Problem \textbf{BVP} for most cases of second-order…

Complementing the analysis in [41], we investigate the well-posedness of SPDEs problems of doubly nonlinear type. These arise ubiquitously in the modelization of dissipative media and correspond to generalized balance laws between…

We propose a novel approach of uncovering Stokes phenomenon exhibited by the holomorphic blocks of $\mathbb{CP}^1$ model by considering it as a specific decoupling limit of SQED$_2$ model. This approach involves using a $\mathbb{Z}_3$…

In this paper we will focus on a parabolic degenerate system with respect to unknown functions u and w on a bounded domain of the two-dimensional Euclidean space. This system appears as a mathematical model for some biological processes.…