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The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…
The solution of the Liouville equation for the ensemble of free particles is presented and the classical analog to the quantum accelerating Airy wave packet is constructed and discussed. Considering the motion of various classical packets…
This paper studies the upper and lower bounds of the lifespan for the classical solutions to the initial value problems of one dimensional wave equations with non-autonomous semilinear terms including the space-derivative of the unknown…
A unifying principle explaining the numerical bounds of quantum correlations remains elusive despite the efforts devoted to identifying it. Here we show that these bounds are indeed not exclusive to quantum theory: for any abstract…
This paper is concerned with the Riemann problem of one-dimensional Euler equations with a singular source. The exact solution of this Riemann problem contains a stationary discontinuity induced by the singular source, which is different…
In this paper, for compressible Euler equations in multiple space dimensions, we prove the break-down of classical solutions with a large class of initial data by tracking the propagation of radially symmetric expanding wave including…
Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical…
In this paper, we study the lifespan estimates of classical solutions for semilinear wave equations with characteristic weights and compactly supported data in one space dimension. The results include those for weights by time-variable, but…
The analysis of the Helmholtz equation is shown to lead to an exact Hamiltonian system of equations describing in terms of ray trajectories a very wide family of wave-like phenomena (including diffraction and interference) going much beyond…
We study the Cauchy problem for classical and weak shock-forming solutions to a model quasilinear wave equation in $1+1$ dimensions arising from a convenient choice of $C^{\infty}$ initial data, which allows us to solve the equation using…
The fundamental solution of the classical approximation of a three waves kinetic equation that happens in the kinetic theory of a condensed gas of bosons near the critical temperature is obtained. It is also proved to be unique in a…
We prove the persistence of analyticity for classical solution of the Cauchy problem for quasilinear wave equations with analytic data. Our results show that the analyticity of solutions, stated by the Cauchy-Kowalewski and…
We present a scaling technique which transforms the evolution problem for a nonlinear wave equation with small initial data to a linear wave equation with a distributional source. The exact solution of the latter uniformly approximates the…
Starting from the von Neumann-Maxwell equations for the Wigner quasi-probability distribution and for the self-consistent electric field, the quantum analog of the classical single-wave model has been derived. The linear stability of the…
The general classical solution of the 3D electromagnetic pp-wave spacetime has been obtained. The relevant line element contains an arbitrary essential function providing an infinite number of in-equivalent geometries as solutions. A…
In this paper, the classical Schr\"odinger equation, which allows the study of classical dynamics in terms of wave functions, is analyzed theoretically and numerically. First, departing from classical (Newtonian) mechanics, and assuming an…
This paper is concerned with the small smooth data problem for the 3-D nonlinear wave equation $\partial_t^2u-\left (1+u+\p_t u\right)\Delta u=0$. This equation is prototypical of the more general equation $\dsize\sum_{i,j=0}^3g_{ij}(u,…
We give one more proof in two and three space dimensions that the irregular solution of the Schrodinger equation, for zero angular momentum, is in fact the solution of an equation containing an extra 'delta function'. We propose another…
The classical limit of wave quantum mechanics is analyzed. It is shown that the general requirements of continuity and finiteness to the solution $\psi(x)=Ae^{i\phi(x)}+ Be^{-i\phi(x)}$, where $\phi(x)=\frac 1\hbar W(x)$ and $W(x)$ is the…
The Whitham equation is a model for the evolution of small-amplitude, unidirectional waves of all wavelengths on shallow water. It has been shown to accurately model the evolution of waves in laboratory experiments. We compute…