相关论文: Periodic motions galore: How to modify nonlinear e…
A new model for evolving Evolutionary Algorithms (EAs) is proposed in this paper. The model is based on the Multi Expression Programming (MEP) technique. Each MEP chromosome encodes an evolutionary pattern that is repeatedly used for…
A proposal is made for a mathematically unambiguous treatment of evolution in the presence of closed timelike curves. In constrast to other proposals for handling the naively nonunitary evolution that is often present in such situations,…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
We represent an algorithm reducing a big class of systems of ($M+1$)-dimensional nonlinear partial differential equations (PDEs) to the systems of $M$-dimensional first order PDEs. Thus, we integrate the original system with respect to only…
The properties of the evolution equation have been analyzed. The uniqueness and the existence of solution for the evolution equation with special value of parameter characterizing intensity of change of external conditions, of the…
Sampling equation method is presented to look for exact solutions of nonlinear differential equations. Application of this approach to one of the extensive chaos model is considered. Exact solutions of this model in travelling wave are…
A method based on infinite parameter conservation laws is described to factor linear differential operators out of nonlinear partial differential equations (PDEs) or out of differential consequences of nonlinear PDEs. This includes a…
Evolutionary algorithms have been successfully applied to a variety of optimisation problems in stationary environments. However, many real world optimisation problems are set in dynamic environments where the success criteria shifts…
Periodic waves are standing wave solutions of nonlinear Schr\''odinger equations whose profile is periodic in space dimension one. We consider general nonlinearities and provide variational characterizations for the periodic wave profiles.…
Finding the optimal parameter setting (i.e. the optimal population size, the optimal mutation probability, the optimal evolutionary model etc) for an Evolutionary Algorithm (EA) is a difficult task. Instead of evolving only the parameters…
Generalized models provide a framework for the study of evolution equations without specifying all functional forms. The generalized formulation of problems has been shown to facilitate the analytical investigation of local dynamics and has…
The family of fifth order nonlinear evolution equations is studied. Some traveling wave elliptic solutions are found. The classification of these exact solutions is given.
Modelling real world systems frequently requires the solution of systems of nonlinear equations. A number of approaches have been suggested and developed for this computational problem. However, it is also possible to attempt solutions…
Asymptotic properties of solutions of odd-order nonlinear dispersion equations are studied. The global in time similarity solutions, which lead to eigenfunctions of the rescaled ODEs, are constructed.
New contributions in the field of iterative optimisation heuristics are often made in an iterative manner. Novel algorithmic ideas are not proposed in isolation, but usually as an extension of a preexisting algorithm. Although these…
When mathematical/computational problems reach infinity, extending analysis and/or numerical computation beyond it becomes a notorious challenge. We suggest that, upon suitable singular transformations (that can in principle be…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
We study a homogenisation problem for problems of mixed type in the framework of evolutionary equations. The change of type is highly oscillatory. The numerical treatment is done by a discontinuous Galerkin method in time and a continuous…
For a large class of nonlinear evolution PDEs, and more generally, of nonlinear semigroups, as well as their approximating numerical methods, two rather natural stability type convergence conditions are given, one being necessary, while the…
Real world problems always have different multiple solutions. For instance, optical engineers need to tune the recording parameters to get as many optimal solutions as possible for multiple trials in the varied-line-spacing holographic…