相关论文: BLP dissipative structures in plane

In this paper, we show uniqueness and stability for the piecewise-smooth solutions to the Burgers--Hilbert equation constructed in Bressan and Zhang [Commun. Math. Sci., 15(1):165--184, 2017]. The Burgers--Hilbert equation is…

In this paper we are extending the well known integrability theorems obtained by multiple scale techniques to the case of linearizable difference equations. As an example we apply the theory to the case of a differential-difference…

Finite-dimensional, inviscid equations of hydrodynamics, such as the zero-viscosity, one-dimensional Burgers equation or the three-dimensional incompressible Euler equation, obtained through a Fourier-Galerkin projection,…

We present a new complex non-stationary particle-like solution of the non-linear Klein-Gordon equation with several spatial variables. The construction is based on reduction to an ordinary differential equation.

We announce a new bi-Hamiltonian integrable two-component system admitting the scalar 3rd-order Burgers equation as a reduction.

We study the BS model, which is a one-dimensional lattice field theory taking real values. Its dynamics is governed by coupled differential equations plus random nearest neighbor exchanges. The BS model has exactly two locally conserved…

This work concerns about stochastic Burgers type equations with reflection. First of all, by means of the equicontinuous uniform Laplace principle, we prove the Freidlin-Wentzell uniform large deviation principle for these equations…

The solution of self-similar shock dynamics satisfying the inviscid Burgers equation are provided in closed form for planar, cylindrical and spherical problems. The approach follows Lee's method for obtaining self-similar solutions for the…

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…

We provide a constructive global existence proof for the multivariate viscous Burgers equation system defined on the whole space or on a domain isomorphic to the n-torus and with time horizon up to infinity and C^{\infty}- data (satisfying…

A two-dimensional cellular automaton(CA) associated with a two-dimensional Burgers equation is presented. The 2D Burgers equation is an integrable generalization of the well-known Burgers equation, and is transformed into a 2D diffusion…

Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an…

We introduce and study a novel generalization of the classical Bin Packing Problem (BPP), called the Bin Packing Problem with Setups (BPPS). In this problem, which has many practical applications in production planning and logistics, the…

The Hirota bilinear difference equation is generalized to discrete space of arbitrary dimension. Solutions to the nonlinear difference equations can be obtained via B\"acklund transformation of the corresponding linear problems.

In this paper, we find a regularized approximate solution for an inverse problem for the Burgers' equation. The solution of the inverse problem for the Burgers' equation is ill-posed, i.e., the solution does not depend continuously on the…

Solutions to finite-dimensional (all spatial Fourier modes set to zero beyond a finite wavenumber $K_G$), inviscid equations of hydrodynamics at long times are known to be at variance with those obtained for the original infinite…

This paper is devoted to the study of initial-boundary value problems for time-fractional analogues of Korteweg-de Vries, Benjamin-Bona-Mahony, Burgers, Rosenau, Camassa-Holm, Degasperis-Procesi, Ostrovsky and time-fractional modified…

A representation of the solid angle and the Burgers formula as line integral is derived in the framework of the theory of gradient elasticity of Helmholtz type. The gradient version of the Eshelby-deWit representation of the Burgers formula…

We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in its first kind form have only cubic and quadratic terms. Then,…

This note addresses input-to-state stability (ISS) properties with respect to (w.r.t.) boundary and in-domain disturbances for Burgers' equation. The developed approach is a combination of the method of De~Giorgi iteration and the technique…