Related papers: Nonlinear Klein-Gordon equation fot nanoscale heat…
In this paper the interaction of attosecond laser pulses with matter is investigated. The scattering and potential motion of heat carriers as well as the external force are considered. Depending on the ratio of the scatterings and potential…
In this paper the Boltzmann transport equation for thermal processes induced by ultra-short laser pulses is formulated and solved. For thermal process where the duration of the laser pulse (femtoseconds - attoseconds) is shorter than the…
In this paper we discuss some exact results related to the fractional Klein--Gordon equation involving fractional powers of the D'Alembert operator. By means of a space-time transformation, we reduce the fractional Klein--Gordon equation to…
In this paper the thermal transport phenomena in MEMS are investigated. The thermal Klein-Gordon transport equation for nanoscale structures is formulated and solved. Key words: MEMS, Klein-Gordon equation, Casimir effect.
In this paper, developing a new approach based on Fourier analysis methods for dispersive PDEs, we establish a low regularity NLS approximation for the one-dimensional cubic Klein-Gordon equation. Our main result includes energy class…
Relaxation dynamics of embedded metal nanoparticles after ultrafast laser pulse excitation is driven by thermal phenomena of different origins the accurate description of which is crucial for interpreting experimental results: hot electron…
We derive approximate expressions for the dispersion relation of the nonlinear Klein-Gordon equation in the case of strong nonlinearities using a method based on the Linear Delta Expansion. All the results obtained in this article are fully…
Fascinating developments in optical pulse engineering over the last 20 years lead to the generation of laser pulses as short as few femtosecond, providing a unique tool for high resolution time domain spectroscopy. However, a number of the…
In this paper the quantum limit of heat transport induced by ultrashort laser pulses is discussed. The new quantum heat transport equation is derived. The relaxation time tau and diffusion coefficient D^e are calculated.
A technique for obtaining an approximate breather solution of the Klein-Gordon equation is presented. A breather solution of the equation describing the propagation of nonlinear waves in a graphene-based superlattice is investigated.
In this paper the dynamics of the interaction of attosecond laser pulses with matter is investigated. It will be shown that the master equation: modified Klein-Gordon equation describes the propagation of the heatons. Heatons are the…
In the paper we present a functional-discrete method for solving the Goursat problem for nonlinear Klein-Gordon equation. The sufficient conditions providing that the proposed method converges superexponentially are obtained. The results of…
A system of nonlocal electron-transport equations for small perturbations in a magnetized plasma is derived using the systematic closure procedure of V. Yu. Bychenkov et al., Phys. Rev. Lett. 75, 4405 (1995). Solution to the linearized…
A detailed consideration of the Klein-Gordon equation in relativistic quantum mechanics is presented in order to offer more clarity than many standard approaches. The equation is frequently employed in the research literature, even though…
In this paper the heat transport in carbon nanotubes is investigated. When the dimension of the structure is of the order of the de Broglie wave length the transport phenomena must be analyzed within quantum mechanics. In this paper we…
In this paper the interaction of ultrashort laser pulses with matter is investigated. The scattering and potential motion of heat carriers, as well as the external force are considered. It is shown that the heat transport is described by…
In this article one will discuss the system of coupled nonlinear Klein-Gordon equations with different velocities and different masses. The nonlinearity considered is a general quadratic nonlinearity without any restriction. The method is a…
We present a new complex non-stationary particle-like solution of the non-linear Klein-Gordon equation with several spatial variables. The construction is based on reduction to an ordinary differential equation.
We study the the nonlinear Klein-Gordon (NLKG) equation on a manifold $M$ in the nonrelativistic limit, namely as the speed of light $c$ tends to infinity. In particular, we consider an order-$r$ normalized approximation of NLKG (which…
We establish asymptotic diffusion limits of the non-classical transport equation derived in [E. W. Larsen, A generalized Boltzmann equation for non-classical particle transport, Joint international topical meeting on mathematics &…