Related papers: Numerical study of Davey-Stewartson I systems
We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their well-posedness and describe some…
This study employs spectral methods to capture the behaviour of wave equation with dispersive-nonlinearity. We describe the evolution of hump initial data and track the conservation of the mass and energy functionals. The…
In this paper, we consider some blow-up problems for the 1D Euler equation with time and space dependent damping. We investigate sufficient conditions on initial data and the rate of spatial or time-like decay of the coefficient of damping…
The initial value problem for the homogeneous Schr\"odinger equation is investigated for radially symmetric initial data with slow decay rates and not too wild oscillations. Our global wellposedness results apply to initial data for which…
Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black…
In this work we establish a dispersive blow-up result for the initial value problem (IVP) for the coupled Schr\"odinger-fifth order Korteweg-de Vries system \begin{align*} \left. \begin{array}{rl} i u_t+\partial_x^2 u &\hspace{-2mm}=\alpha…
In the present study we are interested in the Davey-Stewartson equations (DSE) that model packets of surface and capillary-gravity waves. We focus on the elliptic-elliptic case, for which it is known that DSE may develop a finite-time…
This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…
Recently, the nonlinearity continuation method has been used to numerically solve boundary value problems for steady-state Richards equation. The method can be considered as a predictor-corrector procedure with the simplest form which has…
We consider the hyperbolic-elliptic version of the Davey-Stewartson system with cubic nonlinearity posed on the two dimensional torus. A natural setting for studying blow up solutions for this equation takes place in $H^s, 1/2 < s < 1$. In…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
We study the general (2+1)-dimensional Davey-Stewartson (DS) equations with nonlinear and gain terms and acquire explicit solutions through variable separation approach. In particular, we deduce some main novel excitations for the DS…
In this paper, we conduct a numerical analysis of the strong stabilization and polynomial decay of solutions for the initial boundary value problem associated with a system that models the dynamics of a mixture of two rigid solids with…
The Davey-Stewartson (DS) equations with a perturbation term are presented by taking a fluid system as an example on an uneven bottom. Stability of dromions, solutions of the DS equations with localized structures, against the perturbation…
This article explains and illustrates the use of a set of coupled dynamical equations, second order in a fictitious time, which converges to solutions of stationary Schr\"{o}dinger equations with additional constraints. We include three…
A new and very general technique for simulating solid-fluid suspensions is described; its most important feature is that the computational cost scales linearly with the number of particles. The method combines Newtonian dynamics of the…
The integrable focusing Davey-Stewarson (DS) equations, multidimensional generalizations of the focusing cubic nonlinear Schr\"odinger (NLS) equation, provide ideal mathematical models for describing analytically the dynamics of 2+1…
Several new methods of numerical integration of Cauchy problems with blow-up solutions for nonlinear ordinary differential equations of the first- and second-order are described. Solutions of such problems have singularities whose positions…
This paper is concerned with the analysis of blow-up solutions to the elliptic-elliptic Davey-Stewartson system, which appears in the description of the evolution of surface water waves. We prove a mass concentration property for…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…