Related papers: Solving equations in dense Sidon sets
It is shown that multisoliton solutions of several well known nonlinear PDEs(x, t) can be obtained by certain separation of variables: each n-soliton arises from a mutual solution of a nonlinear ODE(x), common for all NPDEs considered, and…
Polynomial optimization problems represent a wide class of optimization problems, with a large number of real-world applications. Current approaches for polynomial optimization, such as the sum of squares (SOS) method, rely on large-scale…
In this paper, we examine the complex sine-Gordon model in the presence of a boundary, and derive boundary conditions that preserve integrability. We present soliton and breather solutions, investigate the scattering of particles and…
We study translative integral formulas for certain translation invariant functionals on convex polytopes and discuss local extensions and applications to Poisson processes and Boolean models.
We consider the Cauchy problem in the Euclidean space for a doubly degenerate parabolic equation with a space-dependent exponential weight, where the exponent satisfies the doubling condition. In particular, both the so called logconvex and…
Modons, or dipolar vortices, are common and long-lived features of the upper ocean, consisting of a pair of monopolar vortices moving through self-advection. Such structures remain stable over long times and may be important for fluid…
We develop techniques to convexify a set that is invariant under permutation and/or change of sign of variables and discuss applications of these results. First, we convexify the intersection of the unit ball of a permutation and…
In this note we investigate the set $S(n)$ of positive integer solutions of the title Diophantine equation. In particular, for a given $n$ we prove boundedness of the number of solutions, give precise upper bound on the common value of…
We present an alternative proof of Sanov's theorem for Polish spaces in the weak topology that follows via discretization arguments. We combine the simpler version of Sanov's Theorem for discrete finite spaces and well chosen finite…
We prove a dispersive estimate for the solutions of the linearized Water-Waves equations in dimension 1 in presence of a flat bottom. We prove a decay with respect to time t of order 1/3 for solutions with initial data in weighted Sobolev…
New versions and extensions of Benson's outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each…
We extend the classical deconvolution framework in Rn to the case with a pseudodifferential-like solution operator with a symbol depending on both the base and cotangent variable. Our framework enables deconvolution with spatially varying…
It has been proved by S.L.Ziglin, for a large class of 2-degree-of-freedom (d.o.f) Hamiltonian systems, that transverse intersections of the invariant manifolds of saddle fixed points imply infinite branching of solutions in the complex…
Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift are considered. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and…
We give asymptotic sharp estimates for the cardinality of a set of residue classes with the property that the representation function is bounded by a prescribed number. We then use this to obtain an analogous result for sets of integers,…
In this note we present some results that were already conjectured in the work [9] by Bildhauer, Fuchs and Weickert, where they have investigated analytical aspects of coupled variational models with applications to mathematical imaging.…
We study the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazhanov-Stroganov Lax operator. The results apply as well to the spectral analysis of the…
This paper is addressed to the well-posedness of some linear and semilinear backward stochastic differential equations with general filtration, without using the Martingale Representation Theorem. The point of our approach is to introduce a…
In this paper, we consider group classification of local and quasi-local symmetries for a general fourth-order evolution equations in one spatial variable. Following the approach developed by Zhdanov and Lahno, we construct all inequivalent…
In a transformation method the numerical solution of a given boundary value problem is obtained by solving one or more related initial value problems. This paper is concerned with the application of the iterative transformation method to…