Marek Jaworski

The structure of cyclohexane, F-, Cl-, Br- and I-cyclohexane

Abstract The ground state, r0, and the average, r∗ , structures of cyclohexane were determined from the recently reported rotational constants for several isotopic species of cyclohexane. These structures provide a better description of the heavy atom skeleton in cyclohexane than the rs structure and allow an accurate prediction of the rotational constants for C6H12 and C6D12. The new structure for cyclohexane was combined with ab initio calculations to redetermine the key structural features of F-, Cl-, Br- and I-cyclohexane, and it is found that while the equatorial CX bond lengths are comparable with those for secondary substitution in propane, the axial bond lengths are all longer and halfway between those for secondary and tertiary substitution.

Positon and positon-like solutions of the Korteweg-de Vries and Sine-Gordon equations

Abstract It is shown that the positon solution, reported recently for the Korteweg-de Vries and other completely integrable equations, can be regarded as a limiting case of the well-known 2-soliton formula. The existence of integrals of motion related to singular positon solutions is also discussed.

Breather-like solution of the Korteweg-de Vries equation

Abstract A new real singular solution of the Korteweg-de Vries equation is briefly described. It is shown that the spectrum of the associated linear problem consists of a pair of complex conjugate eigenvalues. The existence of constants of motion and eigenfunction normalization integral is also discussed.

Kink-phonon interaction in the Sine-Gordon system

Abstract The nonlinear interaction of a kink and large-amplitude (anharmonic) phonons is described by an exact soliton-periodic solution of the sine-Gordon equation. It is shown that the general kink-phonon solution tends to the well-known perturbation formula when the phonon amplitude tends to zero.

A note on singular solutions of the Koteweg-de Vries equation

Abstract Relations between rational, soliton, periodic and various mixed solutions of the Korteweg-de Vries equation are briefly discussed. It is also shown that the complex spectrum structure can be found for a certain class of real singular quasi-periodic solutions.

Flux-flow dynamics in a long Josephson junction with nonuniform bias current

The flux-flow dynamics in a long Josephson junction is investigated for a spatially nonuniform bias current density. Starting from the linearization about a rotating background, a simple approximate solution of the modified sine–Gordon equation is presented, making possible to derive the current–voltage characteristic of the junction. As an example of nonuniform driving, an overlap structure with an unbiased tail is discussed. In particular, it is shown how a nonuniform distribution of the bias current density may affect the dynamical resistance of a flux-flow oscillator. Analytical results are compared with direct numerical simulations and good agreement is found for a wide range of junction dimensions.

Quasi-periodic solutions of the sine-Gordon equation

Abstract Two-phase quasi-periodic solutions of the sine-Gordon equation are discussed. It is shown that the solutions expressed by the multidimensional θ-function form a broader class than the well-known factorised solutions 4 arctan [ f ( u ) g ( v )]. Expressions describing the spatial and temporal period are also given.

Flux-flow mode in the sine-Gordon system

Abstract An inverse transformation of the theta function is derived, making it possible to investigate a multiperiodic solution of the sine-Gordon equation in the limit of a dense sequence of overlapping solitons. A special case of a unidirectional soliton train interacting with small-amplitude quasi-linear oscillations is discussed as a simple model of the flux-flow state in a long one-dimensional Josephson junction. Approximate analytical solutions for the dispersion parameters are compared with numerical results.

Surface losses and self-pumping effects in a long Josephson junction: A semianalytical approach

The flux-flow dynamics in a long Josephson junction is studied both analytically and numerically. A realistic model of the junction is considered by taking into account a nonuniform current distribution, surface losses, and self-pumping effects. An approximate analytical solution of the modified sine-Gordon equation is derived in the form of a unidirectional dense fluxon train accompanied by two oppositely directed plasma waves. Next, some macroscopic time-averaged quantities are calculated making possible to evaluate the current-voltage characteristic of the junction. The results obtained by the present method are compared with direct numerical simulations both for the current-voltage characteristics and for the loss factor modulated spatially due to the self-pumping. The comparison shows very good agreement for typical junction parameters but indicates also some limitations of the method.

Influence of self-fields on the flux-flow dynamics in a long Josephson junction

The flux-flow dynamics in a long Josephson junction is studied for the in-line and overlap geometry. A simple analytical model, reported recently for the overlap case, is extended to include asymmetric boundary conditions resulting from the self-field effects. Analytical results are compared with numerical simulations both for the magnetic field patterns within the junction and for the current–voltage (I–V) characteristics. It is shown that, depending on the junction geometry, the self-field distribution may affect considerably the fluxon dynamics and consequently working conditions of the flux-flow oscillator.