相关论文: Periodic Solutions to Painlev\'e VI and Dynamical …
We give an extension of the two-component KP hierarchy by considering additional time variables. We obtain the linear $2\times 2$ system by taking into consideration the hierarchy through a reduction procedure. The Lax pair of the…
We prove the existence of small amplitude periodic solutions, for a large Lebesgue measure set of frequencies, in the nonlinear beam equation with a weak quadratic and velocity dependent nonlinearity and with Dirichlet boundary conditions.…
We investigate the points of constancy in the piecewise constant solution profiles of the periodic linearized Korteweg--deVries equation with step function initial data at rational times. The solution formulas are given by certain Weyl…
We consider a class of nonlinear Fokker-Planck equations describing the dynamics of an infinite population of units within mean-field interaction. Relying on a slow-fast viewpoint and on the theory of approximately invariant manifolds we…
A method is described to solve the Poisson problem for a three dimensional source distribution that is periodic into one direction. Perpendicular to the direction of periodicity a free space (or open) boundary is realized. In beam physics,…
We describe all finite orbits of an action of the extended modular group $\bar{\Lambda}$ on conjugacy classes of SL(2,C)-triples. The result is used to classify all algebraic solutions of the general Painleve VI equation up to parameter…
We consider solutions of a discrete Painlev\'e equation arising from a construction of quantum minimal surfaces by Arnlind, Hoppe and Kontsevich, and in earlier work of Cornalba and Taylor on static membranes. While the discrete equation…
We consider Kirchhoff equations for vibrating bodies in any dimension in presence of a time-periodic external forcing with period 2pi/omega and amplitude epsilon, both for Dirichlet and for space-periodic boundary conditions. We prove…
A new iterative method is developed to numerically calculate the periodic, matched beam envelope solution of the coupled Kapchinskij-Vladimirskij (KV) equations describing the transverse evolution of a beam in a periodic, linear focusing…
Existence and stability of time periodic solutions for nonlinear elastic wave equations with viscoelastic terms are established. The existence of the time periodic solution is proved using the spectral decomposition of the linear principal…
Cubic and quartic non-autonomous differential equations with continuous piecewise linear coefficients are considered. The main concern is to find the maximum possible multiplicity of periodic solutions. For many classes, we show that the…
Using continuation methods and bifurcation theory, we study the exact multiplicity of periodic solutions, and the global solution structure, for periodic problems of first order. The results are applied to a population model with fishing,…
In this paper, we give the definition of the random periodic solutions of random dynamical systems. We prove the existence of such periodic solutions for a $C^1$ perfect cocycle on a cylinder using a random invariant set, the Lyapunov…
In this paper, we study the Darboux equations in both classical and system form, which give the elliptic Painlev\'e VI equations by the isomonodromy deformation method. Then we establish the full correspondence between the special Darboux…
The existence and multiplicity of positive periodic solutions for second order non-autonomous singular dynamical systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. Our…
Difference schemes are considered for dynamical systems $ \dot x = f (x) $ with a quadratic right-hand side, which have $t$-symmetry and are reversible. Reversibility is interpreted in the sense that the Cremona transformation is performed…
We consider two different relativistic versions of the Kepler problem in the plane: the first one involves the relativistic differential operator, the second one involves a correction for the usual gravitational potential due to…
We use the middle convolution to obtain some old and new algebraic solutions of the Painlev\'e VI equations.
Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily…
This paper deals with the Vlasov-Stokes' system in three dimensions with periodic boundary conditions in the spatial variable. We prove the existence of a unique strong solution to this two-phase model under the assumption that initial…