Narrow Results

Within the 5D standing wave braneworld model numerical solutions of the equations for matter fields with various spins are found. It is shown that corresponding action integrals are factorizable and convergent over the extra coordinate, i.e. 4D fields are localized on the brane. We find that only left massless fermions are localized on the brane, while the right fermions are localized in the bulk. We demonstrate also quantization of Kaluza–Klein excited modes in our model.

This paper deals with the existence of monotonic traveling and standing wave solutions for a certain class of lattice differential equations. Employing the techniques of monotone iteration coupled with the concept of upper and lower solutions in the theory of monotone dynamical systems, we can classify the monotonic traveling wave solutions with various asymptotic boundary conditions. For the case of zero wave speed, a novel discrete monotone iteration scheme is established for proving the existence of monotonic standing wave solutions. Applications are made to several models including cellular neural networks, original and modified RTD-based cellular neural networks. Numerical simulations of the monotone iteration schemes are also given.

This paper reviews recent results and open problems concerning the existence of steady states to the Maxwell–Schrödinger system. A combination of tools, proofs and results are presented in the framework of the concentration–compactness method.

We investigate the problem of pure gravitational localization of matter fields within the 5D standing wave braneworld generated by gravity coupled to a phantom-like scalar field. We show that in the case of increasing warp factor there exist normalizable zero modes of spin-0, -1/2, -1 and -2 fields on the brane.

The class of nonstationary braneworld models generated by the coupled gravitational and scalar fields is reviewed. The model represents a brane in a spacetime with single time and one large (infinite) and several small (compact) spacelike extra dimensions. In some particular cases the model has the solutions corresponding to the bulk gravi-scalar standing waves bounded by the brane. Pure gravitational localization mechanism of matter particles on the node of standing waves, where the brane is placed, is discussed. Cosmological applications of the model is also considered.

In this paper we are dealing with a Schrödinger–Maxwell system in a bounded domain of R³; the unknowns are the charged standing waves ψ = e^-iωtu(x) in equilibrium with a purely electrostatic potential ϕ. The system is not autonomous, in the sense that the coupling depends on a function q = q(x). The non-homogeneous Neumann boundary condition on ϕ prescribes the flux of the electric field 𝔉 and gives rise to a necessary condition. On the other hand we consider the usual normalizing condition in L² for u. Under mild assumptions involving 𝔉 and the function q = q(x), we prove that this problem has a variational framework: its solutions can be characterized as constrained critical points. Then, by means of the Ljusternick–Schnirelmann theory, we get the existence of infinitely many solutions.

We study the Cauchy problem of an antiferromagnetic spin-1 Bose–Einstein condensate under Ioffe–Pritchard magnetic field $B$. We then address the existence of ground state solutions and characterize the orbit of standing waves.

We study a coupled system of a complex Ginzburg–Landau equation with a quasilinear conservation law

This paper is devoted to the mathematical analysis of a class of nonlinear fractional Schrödinger equations with a general Hartree-type integrand. We show the well-posedness of the associated Cauchy problem and prove the existence and stability of standing waves under suitable assumptions on the nonlinearity. Our proofs rely on a contraction argument in mixed functional spaces and the concentration-compactness method.

A hybrid analytical-numerical method for standing waves in water of any depth exactly satisfies the field equation, the bottom boundary condition, the periodic lateral boundary conditions and the mean water level constraint. The wave height and the kinematic and dynamic free surface boundary conditions are imposed numerically, as a problem in nonlinear optimization. The algorithm is confirmed against an existing fifth-order analytical theory. The method extends the available predictive range for standing waves to near-limit waves in deep, transitional, and shallow water. The limitations of the numerical method are clearly identified. The limit wave cannot be predicted but near-limit extreme wave indicators for wave height, wave number, and crest elevation are defined over the complete range of water depths.

In this paper, a two-dimensional Lagrangian model based on the weakly compressible smoothed particle hydrodynamics (WCSPH) was developed to explore the hydrodynamics of standing waves impinge on a caisson breakwater. The developed model is validated against experimental data and applied then to analyze the wave horizontal velocity in front of a vertical caisson. The effect of wall steepness was investigated in terms of the steady streaming pattern due to generation of fully to partially standing waves. The numerical results indicated that the partially standing waves generated in front of the sloped caisson change the pattern of steady streaming. For the vertical caisson, the velocity component of recirculating cells increased in front of the vertical wall; whereas, for the sloped caisson it decreased from the sloped wall with reducing the wall steepness. In addition, near the milder sloped wall the intensity of velocity component is higher, which is an important parameter in scour process in front of caisson breakwater.