相关论文: Multi-scale Analysis of Nonlinear Equations
We investigate the presence of localized solutions in models described by a single real scalar field with generalized dynamics. The study offers a method to solve very intricate nonlinear ordinary differential equations, and we illustrate…
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…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrodinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying…
Stochastic solutions provide new rigorous results for nonlinear PDE's and, through its local non-grid nature, are a natural tool for parallel computation. There are two different approaches for the construction of stochastic solutions:…
We present a rigorous convergence analysis for cylindrical approximations of nonlinear functionals, functional derivatives, and functional differential equations (FDEs). The purpose of this analysis is twofold: first, we prove that…
We consider a wide class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the normed complex space $(C^{(n)})^m$ of $n\geq r$ times continuously differentiable…
Analyses of peculiar velocity surveys face several challenges, including low signal--to--noise in individual velocity measurements and the presence of small--scale, nonlinear flows. I will present three new analyses that attempt to address…
We analyze the common errors of the recent papers in which the solitary wave solutions of nonlinear differential equations are presented. Seven common errors are formulated and classified. These errors are illustrated by using multiple…
Based on the matrix expression of general nonlinear numerical analogues presented by the present author, this paper proposes a novel philosophy of nonlinear computation and analysis. The nonlinear problems are considered an ill-posed linear…
The expressions of solutions for general $n\times m$ matrix-valued inhomogeneous linear stochastic differential equations are derived. This generalizes a result of Jaschke (2003) for scalar inhomogeneous linear stochastic differential…
We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some…
We introduce the notion of \delta-viscosity solutions for fully nonlinear uniformly parabolic PDE on bounded domains. We prove that \delta-viscosity solutions are uniformly close to the actual viscosity solution. As a consequence we obtain…
We propose a non uniform web spline based finite element analysis for elliptic partial differential equation with the gradient type nonlinearity in their principal coefficients like p-laplacian equation and Quasi-Newtonian fluid flow…
New method is presented to look for exact solutions of nonlinear differential equations. Two basic ideas are at the heart of our approach. One of them is to use the general solutions of the simplest nonlinear differential equations. Another…
We establish some linear and nonlinear integral inequalities of Gronwall-Bellman-Bihari type for functions with two independent variables on general time scales. The results are illustrated with examples, obtained by fixing the time scales…
We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial…
In this paper we discuss the integrability properties of a nonlinear partial difference equation on the square obtained by the multiple scale integrability test from a class of multilinear dispersive equations defined on a four points…
Large-scale simulations of the wave equation in electromagnetism, seismology, and acoustics, can be solved efficiently by finite difference methods. The accuracy of these numerical solutions usually depends on the minimization of…
We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…