Related papers: A Discourse on the Benney Equation
Reaction systems are a formal model that has been introduced to investigate the interactive behaviors of biochemical reactions. Based on the formal framework of reaction systems, we propose new computing models called reaction automata that…
The paper deals with path-dependent Hamilton-Jacobi equations with a coinvariant derivative which arise in investigations of optimal control problems and differential games for neutral-type systems in Hale's form. A viscosity (generalized)…
We consider a reaction-diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction diffusion equations with unbounded time dependent coefficients and different…
A kinetic equation is derived for the phase density of a system of point particles, generating a system of integro-differential equations for distribution functions that have a deterministic meaning. The derivation took into account the…
We study periodic solutions for a quasi-linear system, which is the so called dispersionless Lax reduction of the Benney moments chain. This question naturally arises in search of integrable Hamiltonian systems of the form $ H=p^2/2+u(q,t)…
The inadequacy of Li\'{e}nard-Wiechert potentials is demonstrated as one of the examples related to the inconsistency of the conventional classical electrodynamics. The insufficiency of the Faraday-Maxwell concept to describe the whole…
An exact closed relativistic kinetic equation is derived for a system of identical classical particles interacting with each other through a scalar field. The microscopic deterministic mechanism of the irreversible equilibration process in…
Mechanisms are elucidated underlying the existence of dynamical systems whose generic solutions approach asymptotically (at large time) isochronous evolutions: all their dependent variables tend asymptotically to functions periodic with the…
Short time existence of classical solutions is proved for a system of equations that involves a three excitations kinetic operator. The system is related to the description of a gas of bosons below but close to the critical temperature,…
We study the representation formulae for the fundamental solutions and viscosity solutions of the Hamilton-Jacobi equations of contact type. We also obtain a vanishing contact structure result for relevant Cauchy problems which can be…
The asymptotic stability of a global solution satisfying Hamilton-Jacobi equations with jumps will be analyzed in dependence on the strong dissipativity of the jump control function and using orbits of the differentiable flows to describe…
For $N$-body problems with homogeneous potentials we define a special class of central configurations related with the reduction of homotheties in the study of homogeneous weak KAM solutions. For potentials in $1/r^\alpha$ with $\alpha\in…
A convenient algebraic structure to describe some forms of dynamics of two hamiltonian systems with nonpotential (magnetic--type) interaction is considered. An algebraic mechanism of generation of such dynamics is explored on simple "toy"…
Using the Clifford and the Spin-Clifford formalisms we prove that the classical relativistic Hamilton Jacobi equation for a charged massive (and spinning) particle interacting with an external electromagnetic field is equivalent to a…
We present a theory for the construction of renormalized kinetic equations to describe the dynamics of classical systems of particles in or out of equilibrium. A closed, self-consistent set of evolution equations is derived for the…
We can incorporate a "time" evolution into thermodynamics as a Hamilton-Jacobi dynamics. A set of the equations of states in thermodynamics is considered as the generalized eikonal equation, which is equivalent to Hamilton-Jacobi equation.…
In our previous papers [11,13] we showed that the Hamilton-Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. We also showed how…
We argue that Hamilton-Jacobi equations provide a convenient and intuitive approach for studying the large-scale behavior of mean-field disordered systems. This point of view is illustrated on the problem of inference of a rank-one matrix.…
The system of particles interacting via multibody interatomic potential of general form is considered. Possible variants of partition of the total force acting on a single particle into pair contributions are discussed. Two definitions for…
We analyze the behavior of a quantum system described by a one-dimensional asymmetric potential consisting of a step plus a harmonic barrier. We solve the eigenvalue equation by the integral representation method, which allows us to…