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

We deal with a mechanism of generating distributional chaos in planar nonautonomous ODEs and try to measure chaosity in terms of topological entropy. It is based on the interplay between simple periodic solutions. We prove the existence of…

We consider several ways of how one could classify the various types of soliton solutions related to nonlinear evolution equations which are solvable by the inverse scattering method. In doing so we make use of the fundamental analytic…

Crossover and mutation are the two main operators that lead to new solutions in evolutionary approaches. In this article, a new method of performing the crossover phase is presented. The problem of choice is evolutionary decision tree…

Ordinary Differential Equations are generally too complex to be solved analytically. Approximations thereof can be obtained by general purpose numerical methods. However, even though accurate schemes have been developed, they remain…

Differential-elimination algorithms apply a finite number of differentiations and eliminations to systems of partial differential equations. For systems that are polynomially nonlinear with rational number coefficients, they guarantee the…

This work studies a variational formulation and numerical solution of a regularized morphoelasticity problem of shape evolution. The foundation of our analysis is based on the governing equations of linear elasticity, extended to account…

Some interesting (periodic!) solutions of certain systems of $4$ nonlinear Ordinary Differential Equations $dx_{n}\left( t\right) /dt=P_{2}^{\left( n\right) }\left[ x_{m}\left( t\right) \right] /\left[ x_{1}\left( t\right) +x_{2}\left(…

In the real world, there exist a class of optimization problems that multiple (local) optimal solutions in the solution space correspond to a single point in the objective space. In this paper, we theoretically show that for such multimodal…

We present an analytical solution for triad nonlinear evolution equations with modified Schr\"odinger terms. An example for application in compressible water waves is presented.

We prove the existence of multiple solutions for a quasilinear elliptic equation containing a term with natural growth, under assumptions that are invariant by diffeomorphism. To this purpose we develop an adaptation of degree theory.

Multi-Objective Evolutionary Algorithms (MOEAs) have been proved efficient to deal with Multi-objective Optimization Problems (MOPs). Until now tens of MOEAs have been proposed. The unified mode would provide a more systematic approach to…

We present a general framework to describe the evolutionary dynamics of an arbitrary number of types in finite populations based on stochastic differential equations (SDE). For large, but finite populations this allows to include…

We study the homogenization property of systems of quasi-linear PDEs of parabolic type with periodic coefficients, highly oscillating drift and highly oscillating nonlinear term. To this end, we propose a probabilistic approach based on the…

We consider stochastic equations for the class of formal mappings. Existence and uniqueness of solution, as well as evolution property are proved.

We present a new algorithm for computing hyperexponential solutions of ordinary linear differential equations with polynomial coefficients. The algorithm relies on interpreting formal series solutions at the singular points as analytic…

We study a kind of better recurrence than Kolmogorov's one: periodicity recurrence,which corresponds periodic solutions in distribution for stochastic differential equations. On the basis of technique of upper and lower solutions and…

A novel method is developed for constructing periodic solutions of a model equation describing nonlocal Josephson electrodynamics. This method consists of reducing the equation to a system of linear ordinary differential equations through a…

The paper represents the method for construction of the families of particular solutions to some new classes of $(n+1)$ dimensional nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic…

There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…

We present an algorithm that transforms, if possible, a given ODE or PDE with radical function coefficients into one with rational coefficients by means of a rational change of variables. It also applies to systems of linear ODEs. It is…