Related papers: Potential equivalence transformations for nonlinea…
We review some surprising links which have been discovered in the last few years between the theory of certain ordinary differential equations, and particular integrable lattice models and quantum field theories in two dimensions. An…
A full symmetry classification is given for models of energy transport in radiant plasma when the mass density is spatially variable and the diffusivity is nonlinear. A systematic search for conservation laws also leads to some potential…
The moving coframe method is applied to solve the local equivalence problem for the class of nonlinear wave equations in two independent variables under an action of the pseudo-group of contact transformations. The structure equations and…
We consider a rather general class of evolutionary PDEs involving dissipation (of possibly fractional order), which competes with quadratic nonlinearities on the regularity of the overall equation. This includes as prototype models,…
We study the applicability of the {\it parallel tempering method} (PT) in the investigation of first- order phase transitions. In this method, replicas of the same system are simulated simultaneously at different temperatures and the…
Transformers have been shown to work well for the task of English euphemism disambiguation, in which a potentially euphemistic term (PET) is classified as euphemistic or non-euphemistic in a particular context. In this study, we expand on…
For the equations of the form $y''=P(x,y)+3 Q(x,y) y'+3 R(x,y) {y'}^2 +S(x,y) {y'}^3$ the problem of equivalence in the class of point transformations is considered. Effective procedure for determining the class of point equivalence for the…
$\mathcal{PT}$-symmetric models with a Wick rotation of time ($ t \rightarrow \pm i t$) show spectral phase transitions that are similar to those of dissipative systems driven out of equilibrium. Optics can provide an accessible test bed to…
High-dimensional partial-differential equations (PDEs) arise in a number of fields of science and engineering, where they are used to describe the evolution of joint probability functions. Their examples include the Boltzmann and…
The present paper is devoted to the study of transition fronts in nonlocal reaction-diffusion equations with time heterogeneous nonlinearity of ignition type. It is proven that such an equation admits space monotone transition fronts with…
We investigate the convergence rates of variational posterior distributions for statistical inverse problems involving nonlinear partial differential equations (PDEs). Departing from exact Bayesian inference, variational inference…
Transfer entropy (TE) captures the directed relationships between two variables. Partial transfer entropy (PTE) accounts for the presence of all confounding variables of a multivariate system and infers only about direct causality. However,…
Phase modulation has scarcely been mentioned in diffusive systems since the diffusion process does not carry momentum like waves. Recently, the non-Hermitian physics provides a new perspective for understanding diffusion and shows prospects…
We perform a detailed classification of the Lie point symmetries and of the resulting similarity transformations for the Generalized Boiti-Leon-Pempinelli equations. The latter equations for a system of two nonlinear 1+2 partial…
Fokker-Planck equation with the velocity-dependent coefficients is considered for various isotropic systems on the basis of probability transition (PT) approach. This method provides the self-consistent and universal description of friction…
We consider a problem of identification of point sources in time dependent advection-diffusion systems with a non-linear reaction term. The linear counterpart of the problem in question can be reduced to solving a system of non-linear…
Q-conditional symmetries (nonclassical symmetries) for a general class of two-component reaction-diffusion systems with constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first type…
Since the parity-time-(PT-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with PT-symmetric potentials have been investigated. However, previous studies of PT-symmetric waves were…
In this paper we introduce, inspired by Clausius and developing the ideas of \cite{pre}, the concept of equivalence of transformations in non equilibrium theory of diffusive systems within the framework of macroscopic fluctuation theory.…
We clarify the notion of effective equivalence and characterize geometrically the effectively equivalent permutation groups. In particular, we present examples showing that the latter do not correspond to affinely equivalent polytopes…