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In bidisperse particle mixtures varying in size or density alone, large particles rise (driven by percolation) and heavy particles sink (driven by buoyancy). When the two particle species differ from each other in both size and density, the…
In this paper we prove the existence and uniqueness of a solution to the nonstationary two dimensional system of equations describing miscible liquids with nonsmooth, multivalued and nonmonotone boundary conditions of subdifferential type.…
We consider an application of modification of our variational-wavelet approach to some nonlinear collective model of beam/plasma physics: Vlasov/Boltzmann-like reduction from general BBGKY hierachy related to modeling of propagation of…
In this paper we study the construction of a discrete solution for a hyperbolic system of partial differentials of the strongly coupled type. In its construction, the discrete separation of matricial variable method was followed. Two…
In this paper, we use Hirota's bilinear method to directly construct periodic wave solutions of nonlinear equations. The asymptotic property of periodic wave solutions are analyzed. It is shown that well-known soliton solutions can be…
A method is presented for obtaining the $\epsilon$-expansion for on-shell massless scalar double-box diagram.
In this paper we investigate the multi-component AB system that comes from the geophysical fluid dynamics. We construct bright-dark soliton solutions through Hirota's bilinear method. For the two-component AB system, asymptotic behaviours…
In this work we employ a recently proposed bifurcation analysis technique, the deflated continuation algorithm, to compute steady-state solitary waveforms in a one-component, two dimensional nonlinear Schr\"odinger equation with a parabolic…
In this paper a randomized version of the Beverton-Holt type discrete model is proposed. Its solution stochastic process and the random steady state are determined. Its first probability density function and second probability density…
This paper studies finite-sample set-membership identification for discrete-time bilinear systems under bounded symmetric log-concave disturbances. Compared with existing finite-sample results for linear systems and related analyses under…
We develop a systematic procedure for constructing soliton solutions of an integrable two-component Camassa-Holm (CH2) system. The parametric representation of the multisoliton solutions is obtained by using a direct method combined with a…
We first construct a $(2+1)$-dimensional negative AKNS hierarchy and then we give all possible local and (discrete) nonlocal reductions of these equations. We find Hirota bilinear forms of the negative AKNS hierarchy and give one- and…
We investigate several models described by real scalar fields, searching for topological defects. Some models are described by a single field, and support one or two topological sectors, and others are two-field models, which support…
Reaction-diffusion equations appear in biology and chemistry, and combine linear diffusion with different kind of reaction terms. Some of them are remarkable from the mathematical point of view, since they admit families of travelling waves…
We prove an existence and uniqueness result for two-obstacle problem for quasilinear Stochastic PDEs (DOSPDEs for short). The method is based on the probabilistic interpretation of the solution by using the backward doubly stochastic…
Microstrata are the non-extremal analogues of superstrata: they are smooth, non-extremal (non-BPS) solitonic solutions to IIB supergravity whose deep-throat limits approximate black holes. Using perturbation theory and numerical methods, we…
In this article we study a system of eikonal equations. Our aim is to isolate the solutions which minimise the discontinuity set of the gradient.
This paper deals with the existence of global weak solutions for a wide class of (multiple species) cross-diffusions systems. The existence is based on two different ingredients: an entropy estimate giving some gradient control and a…
We consider two-component nonlinear dissipative spatially extended systems of reaction-cross-diffusion type. Previously, such systems were shown to support "quasi-soliton" pulses, which have fixed stable structure but can reflect from…
We present a series of experimental investigations on binary mixtures of Bose-Einstein condensates. Our focus lies on the regime where the interaction parameters place the system at the threshold of miscibility. We demonstrate that the…