Solitons and conservation laws of Klein–Gordon equation with power law and log law nonlinearities

This paper obtains the conservation laws of the Klein–Gordon equation with power law and log law nonlinearities. The multiplier approach with Lie symmetry analysis is employed to obtain the conserved densities. The 1-soliton solutions are subsequently used to compute the conserved quantities from the conserved densities. Later the perturbation terms are added and the conservation laws of the perturbed Klein–Gordon equation are studied.     

A molecular dynamics study to determine the solid-liquid interfacial tension using test area simulation method (TASM)

Molecular dynamics (MD) studies on heat transfer from a heated nanoparticle into the surrounding fluid have indicated that the fluid next to a spherical nanoparticle can get heated well above its boiling point without observing a phase change, while a contradicting behavior was observed for a flat surface-fluid interface. Another interesting observation is that the critical heat flux was found to increase with increase in the wetting characteristics of solid. Thus, the interfacial tension or free energy of solid-liquid interface could play a pivotal role in the mechanism of heat transfer. A recent study by Gloor et al. [J. Chem. Phys. 123, 134703 (2005)] has proposed test area simulation method (TASM) for the determination of interfacial tension. The present study involves the determination and the comparison of solid-liquid interfacial tension for planar and spherical interfaces using MD based on TASM and analyze the results. A higher interfacial tension value is observed for spherical nanoparticle fluid interface compared to flat surface fluid interface. The results also indicate that the solid-liquid interfacial tension is a size and temperature dependent property. The results from this study are also expected to give better insights into the possible reasons for the observed differences in the thermal transport for spherical nanoparticle-liquid interface compared to planar-liquid interface.     

Nonlinear evolution equations for surface plasmons for nano-focusing at a Kerr/metallic interface and tapered waveguide

Maxwell's equations for a metallic and nonlinear Kerr interface waveguide at the nanoscale can be approximated to a (1+1) D Nonlinear Schrodinger type model equation (NLSE) with appropriate assumptions and approximations. Theoretically, without losses or perturbations spatial plasmon solitons profiles are easily produced. However, with losses, the amplitude or beam profile is no longer stationary and adiabatic parameters have to be considered to understand propagation. For this model, adiabatic parameters are calculated considering losses resulting in linear differential coupled integral equations with constant definite integral coefficients not dependent on the transverse and longitudinal coordinates. Furthermore, by considering another configuration, a waveguide that is an M–NL–M (metal–nonlinear Kerr–metal) that tapers, the tapering can balance the loss experienced at a non-tapered metal/nonlinear Kerr interface causing attenuation of the beam profile, so these spatial plasmon solitons can be produced. In this paper taking into consideration the (1+1)D NLSE model for a tapered waveguide, we derive a one soliton solution based on He's Semi-Inverse Variational Principle (HPV).     

Cnoidal and snoidal wave solutions to coupled nonlinear wave equations by the extended Jacobi’s elliptic function method

This paper studies two nonlinear coupled evolution equations. They are the Zakharov equation and the Davey–Stewartson equation. These equations are studied by the aid of Jacobi’s elliptic function expansion method and exact periodic solutions are extracted. In addition, the Zakharov equation with power law nonlinearity is solved by traveling wave hypothesis.     

Dynamics of solvent and rotational relaxation of glycerol in the nanocavity of reverse micelles

The dynamics of solvent and rotational relaxation of Coumarin 480 and Coumarin 490 in glycerol containing bis-2-ethyl hexyl sulfosuccinate sodium salt (AOT) reverse micelles have been investigated with steady-state and time-resolved fluorescence spectroscopy. We observed slower solvent relaxation of glycerol confined in the nanocavity of AOT reverse micelles compared to that in pure glycerol. However, the slowing down in the solvation time on going from neat glycerol to glycerol confined reverse micelles is not comparable to that on going from pure water or acetonitrile to water or acetonitrile confined AOT reverse micellar aggregates. While solvent relaxation times were found to decrease with increasing glycerol content in the reverse micellar pool, rotational relaxation times were found to increase with increase in glycerol content.     

P-H and P-P bond activation by Ni(I) and Fe(I) beta-diketiminato-complexes

Reactions of ((NacNac)Ni)2(mu-eta3-eta3-C6H5Me) (NacNac = HC(CMeNC6H3(i-Pr)2)2) with PH2Ph or PHPh2 proceeds in a facile manner to afford the Ni(I)-phosphine adducts (NacNac)Ni(PH2Ph) and (NacNac)Ni(PHPh2) , respectively. The related reactions of the Fe(I) complex (NacNac)Fe(eta2-CH2CPh2) with PH2Ph resulted in the formation of [(NacNac)Fe(mu2-PPh)]2. Alternatively was also obtained from the reaction of [(NacNac)Fe(mu-Cl)]2 with PHPh2 and Na/K. The Ni(II) di-phosphosphine bridged compound [((NacNac)Ni)2(mu4-(PPh)2)] was prepared via reaction of ((NacNac)Ni)2(mu-eta3-eta3-C6H5Me) with P5Ph5. Crystallographic data are reported for compounds .     

Chiral Solitons With Time-Dependent Coefficients

This paper obtains the exact 1-soliton solution to the chiral nonlinear Schrödinger’s equation with time-dependent coefficients. Both bright and dark soliton solutions are obtained. The soliton ansatz method is used to carry out the derivation of the soliton.     

Bound and Scattering States of Extended Calogero Model with an Additional PT Invariant Interaction

Here we discuss two many-particle quantum systems, which are obtained by adding some nonhermitian but PT (i.e. combined parity and time reversal) invariant interaction to the Calogero model with and without confining potential. It is shown that the energy eigenvalues are real for both of these quantum systems. For the case of extended Calogero model with confining potential, we obtain discrete bound states satisfying generalised exclusion statistics. On the other hand, the extended Calogero model without confining term gives rise to scattering states with continuous spectrum. The scattering phase shift for this case is determined through the exchange statistics parameter. We find that, unlike the case of usual Calogero model, the exclusion and exchange statistics parameters differ from each other in the presence of PT invariant interaction.     

Optical solitons: Quasi-stationarity versus Lie transform

This paper is a comparitive study of the two approaches namely the quasi-stationarity and the Lie transform that are used for studying the classical optical solitons along with its perturbations governed by the non-linear Schrödinger's equation with Kerr law of non-linearity. The relative advantages and disadvantages of the two methods are enumerated. The study is conducted with both, Hamiltonian as well as non-Hamiltonian type perturbations.