Related papers: Inferring nonlinear parabolic field equations from…
The article investigates an algorithm for identifying an unknown constant parameter for a scalar regression model using a nonlinear operator that allows us to obtain a new regression equation (with an expanded number of unknown parameters)…
A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible…
Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…
We apply functional analytical and variational methods in order to study well-posedness and qualitative properties of evolution equations on product Hilbert spaces. To this aim we introduce an algebraic formalism for matrices of…
One may ask whether an extended group of invariance can naturally be attributed to the space of associative commutative Quadrahyperbolic Numbers? To search for a rigorous and positive answer to the question, we shall focus on the method of…
A nonlinear model of the scalar field with a coupling between the field and its gradient is developed. It is shown, that such model is suitable for the description of phase transition accompanied by formation of spatial inhomogeneous…
We study the dynamics of a degenerate parabolic equation with a variable, generally non-smooth diffusion coefficient, which may vanish at some points or be unbounded. We show the existence of a global branch of nonnegative stationary…
Many systems of partial differential equations have been proposed as simplified representations of complex collective behaviours in large networks of neurons. In this survey, we briefly discuss their derivations and then review the…
A (2+1)-dimensional quasilinear system is said to be `integrable' if it can be decoupled in infinitely many ways into a pair of compatible n-component one-dimensional systems in Riemann invariants. Exact solutions described by these…
Fluctuation and dissipation dynamics is examined at all temperature ranges for the general case of a background time evolving scalar field coupled to heavy intermediate quantum fields which in turn are coupled to light quantum fields. The…
Periodically forced turbulence is used as a test case to evaluate the predictions of two-equation and multiple-scale turbulence models in unsteady flows. The limitations of the two-equation model are shown to originate in the basic…
We study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the first order divergence operator acting on a flux function, which is related to the spatial gradient of the…
We study dynamics of scalar fields on a large class of geometries described by integrable sigma models. Although equations of motion are not separable due to absence of isometries and Killing tensors, we completely determine the spectra…
We deal with nonlinear systems of parabolic type satisfying component-wise structural conditions. The nonlinear terms are Carath\'eodory maps having controlled growth with respect to the solution and the gradient and the data are in…
Nonlinear systems are capable of displaying complex behavior even if this is the result of a small number of interacting time scales. A widely studied case is when complex dynamics emerges out of a nonlinear system being forced by a simple…
Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. We…
In recent years, a new method for experimental nonlinear modal analysis has been developed, which is based on the extended periodic motion concept. The method is well suited to experimentally obtain amplitude-dependent modal properties…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the…
Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the…