相关论文: Periodic motions galore: How to modify nonlinear e…

We present doubly-periodic solutions of the infinitely extended nonlinear Schrodinger equation with an arbitrary number of higher-order terms and corresponding free real parameters. Solutions have one additional free variable parameter that…

We discuss linear autonomous evolution equations on function spaces which have the property that a positive initial value leads to a solution which initially changes sign, but then becomes - and stays - positive again for sufficiently large…

In the paper we suggest the homotopy method for solving of the non linear evolution equation. This method consists of two steps. First is the analytical solution for the linearized version of the non-linear evolution deep in the saturation…

We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…

Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…

Recently, various evolutionary partial differential equations (PDEs) with a mixed derivative have been emerged and drawn much attention. Nonetheless, their PDE-theoretical and numerical studies are still in their early stage. In this paper,…

In this paper, we present a method to identify integrable complex nonlinear oscillator systems and construct their solutions. For this purpose, we introduce two types of nonlocal transformations which relate specific classes of nonlinear…

In this paper we study nonlinear partial differential equations (PDEs) that are used to model different value adjustments denoted generally as xVA. These adjustments are nowadays commonly added to the risk-free financial derivative values…

A change of variables is introduced to reduce certain nonlinear stochastic evolution equations with multiplicative noise to the corresponding deterministic equation. The result is then used to investigate a stochastic porous medium…

In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…

Semilinear stochastic evolution equations with multiplicative L\'evy noise and monotone nonlinear drift are considered. Unlike other similar work we do not impose coercivity conditions on coefficients. Existence and uniqueness of the mild…

The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…

This paper provides a framework to strong time periodic solutions of quasilinear evolution equations. The novelty of this approach is that zero is allowed to be a spectral value of the underlying linearized operator. This approach is then…

We propose a new approach to the study of (nonlinear) growth and instability for semilinear evolution equations with compact nonlinearities. We show, in particular, that compact nonlinear perturbations of a linear evolution equation can be…

Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential…

Differential evolution (DE) is a well-known type of evolutionary algorithms (EA). Similarly to other EA variants it can suffer from small populations and loose diversity too quickly. This paper presents a new approach to mitigate this…

A new approach for obtaining the transformations of solutions of nonlinear ordinary differential equations representable as the compatibility condition of the overdetermined linear systems is proposed. The corresponding transformations of…

Symmetry groups of PDEs allow to transform solutions continuously into other solutions. In this paper, we use this property for the observability analysis of nonlinear PDEs with input and output. Based on a differential-geometric…

A straightforward algorithm for the symbolic computation of higher-order symmetries of nonlinear evolution equations and lattice equations is presented. The scaling properties of the evolution or lattice equations are used to determine the…

This paper demonstrates that simple yet important characteristics of coevolution can occur in evolutionary algorithms when only a few conditions are met. We find that interaction-based fitness measurements such as fitness (linear) ranking…