Related papers: High-speed kinks in a generalized discrete $\phi^4…
This work investigates twinlike scalar field models that support kinks with the same energy density and stability. We find the first order equations compatible with the equations of motion. We use them to calculate the conditions under…
We have found exact, periodic, time-dependent solitary wave solutions of a discrete $\phi^4$ field theory model. For finite lattices, depending on whether one is considering a repulsive or attractive case, the solutions are either Jacobi…
Most approximation methods in high dimensions exploit smoothness of the function being approximated. These methods provide poor convergence results for non-smooth functions with kinks. For example, such kinks can arise in the uncertainty…
This technical note is concerned with boundary stabilization of multi-dimensional discrete-velocity kinetic models. By exploiting a certain stability structure of the models and adapting an appropriate Lyapunov functional, we derive…
We present a review of our recent works directed towards discovery of a periodic, kink-like and soliton-like travelling wave solutions within the models of transport phenomena and the mathematical biology. Analytical description of these…
Highly localized explicit solutions to multidimensional wave and Klein--Gordon--Fock equations are presented. Their Fourier transform is also found explicitly. Solutions depend on a set of parameters, and demonstrate astigmatic properties.…
We consider the speed planning problem for a vehicle moving along an assigned trajectory, under maximum speed, tangential and lateral acceleration, and jerk constraints. The problem is a nonconvex one, where nonconvexity is due to jerk…
We present a numerical study of the process of the kink-antikink collisions in the coupled one-dimensional two-component $\phi^4$ model. Our results reveal two different soliton solutions which represent double kink configuration and…
The radiation from oscillating kink in (1+1) dimensional relativistic $\phi^4$ model is considered. Both analytical and numerical approaches are presented and the comparison between these methods is discussed. Acceleration of the kink in…
In this paper the whole kink varieties arising in several massive non-linear Sigma models whose target space is the torus ${\mathbb S}^1\times{\mathbb S}^1$ are analytically calculated. This possibility underlies the construction of…
Using a path integral approach, we derive an analytical solution of a nonlinear and singular Langevin equation, which has been introduced previously by P.-G. de Gennes as a simple phenomenological model for the stick-slip motion of a solid…
In this paper, we study the $\phi^4$ kink scattering from a spatially localized $\mathcal{PT}$-symmetric defect and the effect of the kink's internal mode (IM) is discussed. It is demonstrated that if a kink hits the defect from the gain…
First order kinetic mean field games formally describe the Nash equilibria of deterministic differential games where agents control their acceleration, asymptotically in the limit as the number of agents tends to infinity. The known results…
A quench in an underdamped one dimensional $\phi^4$ model is studied by analytical methods. The density of kinks just after the transition is proportional to the square root of the rate of the quench for slow quenches. If the quench is…
This work deals with the presence of topological defects in k-field models, where the dynamics is generalized to include higher order power in the kinetic term. We investigate kinks in (1,1) dimensions and vortices in (2,1) dimensions,…
We demonstrate the existence in the sense of sequences of solutions for some integro-differential type problems involving the drift term and the square of the Laplace operator, on the whole real line or on a finite interval with periodic…
Nonlinear cubic Euler-Lagrange equations of motion in the traveling variable are usually derived from Ginzburg-Landau free energy functionals frequently encountered in several fields of physics. Many authors considered in the past damped…
On a smooth closed manifold $M$, we introduce a novel theory of maximal slope curves for any pair $(\phi,H)$ with $\phi$ a semiconcave function and $H$ a Hamiltonian. By using the notion of maximal slope curve from gradient flow theory, the…
We consider solving a generalized Allen-Cahn equation coupled with a passive convection for a given incompressible velocity field. The numerical scheme consists of the first order accurate stabilized implicit explicit time discretization…
We show explicitly how a strongly coupled fixed point can be constructed in scalar $g\varphi^4$ theory from the solutions to a non-linear eigenvalue problem. The fixed point exists only for $d< 4$, is unstable and characterized by $\nu=2/d$…