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Three-dimensional shallow water waves over an uneven bottom are considered. The depth is assumed to be slow in variation. As a model, an inhomogeneous Kadomtsev-Petviashvili equation is presented. Some reductions of this equation are used to describe deformation of a line soliton due to the depth change. The model equation is valid for a wide class of two-dimensional nonlinear waves in inhomogeneous systems.

A new approach to nonlinear waves in one-dimensional discontinuous media is presented. As a model a nonlinear lattice which has a discontinuity of the mass distribution is considered. Two kinds of physically interesting waves, slowly varying waves and carrier wave modulations, are investigated. For the former (latter), incident, reflected and transmitted waves are described by Korteweg-de Veries (Nonlinear Schrodinger) equations on different coordinates. The reflected and transmitted waves are constructed from the incident wave analytically. Fission and reflection of a soliton due to the discontinuity are explicitly shown in the lowest order.

A coupled nonlinear Schrodinger equation is studied. The equation describes nonlinear modulations of two monochromatic waves whose group velocities are almost equal. As a special case, optical solitons for two linearly polarlized waves are explicitly shown.

Nonlinear wave propagations in one-dimentional inhomogeneous lattices are studied. The force between adjacent particles is anharmonic and the mass distrubution is not uniform. It is assumed that the amplitudes of the waves are small and the variation of the mass distribution is slow. By introducing appropriate transformation of independent and dependent variables, we obtain nonlinear evolution equations for various types, strength and slowness, of inhomogeneities. As an application the influences of impurity and discontinuity on the wave propagation are discussed. Our approach is valid for a large class of nonlinear dispersive inhomogeneous systems.

Wave propagations in nonlinear lattices with random mass distribution are investigated. The following two cases which have important applications are studied; 1) slowly varying waves in a lattice with a cubic nonlinearity, and 2) carrier wave modulations in a lattice with quadratic and cubic nonlinearities. The former and the latter cases reduces to stochastic modified Korteweg-de Vries equation and stochastic nonlinear Schrodinger equation, respectively. Propagations of solitons are analysed for both cases under an assumption that mass distribution is Gaussian and white.

Initial value problem of the unstable nonlinear Schrodinger (UNS) equation i u x + u t t -2| u |^2u=0 w i t h b o u n d a r y c o n d i t i o n |u|→1 (x→±∞), i s s o l v e d b y t h e i n v e r s e s c a t t e r i n g m e t h o d . A s a n a p p l i c a t i o n , d a r k s o l i t o n s o l u t i o n s a r e o b t a i n e d . P o s i t i o n s h i f t d u e t o a c o l l i s i o n o f t w o s o l i t o n s i s s h o w n t o b e a t t r a c t i v e ( r e s . r e p u l s i v e ) w h e n t h e d i r e c t i o n s o f t h e i r v e l o c i t i e s a r e o p p o s i t e ( r e s . s a m e ). I t i s a l s o s h o w n t h a t t h e U N S e q u a t i o n h a s a n i n f i n i t e n u m b e r o f c o n s e r v e d q u a n t i t i e s .

As a canonical equation for soliton phenomena in unstable media, the unstable nonlinear Schrodinger (UNS) equation, i q x + q tt +2| q | 2 q =0 is proposed. The UNS equation is derived for two physical systems, Rayleigh-Taylor instability and electron beam plasma. It is shown that the initial value problem can be solved by the inverse scattering method. The exact N -soliton solution gives information on the soliton interaction: the faster (slower) soliton has negative (positive) position shift. It is thus concluded that soliton interaction in unstable media is attractive. Further, it is reported that the UNS equation explains a recent observation on propagations of localized structures in electron beam plasma.

Recent works on the unstable nonlinear Schrodinger (UNS) equation, iqx+qn+2|q|2q=0, are reviewed. It is shown that initial value problems can be solved by the inverse scattering method. Exact N soliton solutions gives an information on the soliton interaction in unstable media. Namely, the position shifts due to the collisions have opposite signs compared with the conventional nonlinear Schrodinger equation, iqt+qxx + 2|q|2q = 0. As applications of the UNS equation, two physical systems, the Rayleigh-Taylor instability problem and electron beam plasma, are discussed. In both systems, the dispersion relation has a critical wave number below which frequency becomes a complex number. It is shown that near the critical wave number the wave amplitude obeys the UNS equation. It is concluded that the UNS equation is a canonical equation which describes nonlinear modulations of wave amplitude in unstable media.

A nonlinear stage of the two-dimensional Rayleigh-Taylor instability is studied by including the effect of surface tension between the two fluids. By means of the reductive perturbation method, three types of nonlinear evolution equations for the interface are obtained. Each equation is valid within a certain region of the wave number k introduced in the linearized theory. When k is sufficiently large and thus in the stable region, the nonlinear Schrodinger equation is derived. Depending on the value of k in this region, bright or dark solitons exist. When k is nearly equal to the critical wave number k c , the unstable nonlinear Schrodinger equation is obtained. Further, it is shown that a nonlinear diffusion equation is obtained in the unstable region where k is smaller than k c .

The propagation of active waves in a reaction-diffusion system with spatial inhomogeneity is examined using the geometrical shock dynamics method. The refraction or diffraction of active waves is found for the case that the diffusivity of the system changes with a spatial variable.

We demonstrate an important role of the process of optical rectification in the theory of nonlinear wave propagation in quadratically nonlinear [or ${\ensuremath{\chi}}^{(2)}$] periodic optical media. We derive a novel physical model for gap solitons in ${\ensuremath{\chi}}^{(2)}$ nonlinear Bragg gratings.

We demonstrate an important role of the process of optical rectification in the theory of nonlinear wave propagation in quadratically nonlinear [or $\chi^{(2)}$ ] periodic optical media. We derive a novel physical model for gap solitons in $\chi^{(2)}$ nonlinear Bragg gratings., Comment: 3.5 pages, double-column, no figures; submitted to Physical Review E

A genetic routing method for switchbox problem with novel coding technique is presented. The principle of proposed method and results of computer experiments are described in detail.

We have investigated the magnetic field dependence of the Josephson tunnel junctions whose shape is defined with a normal-distribution function. It was revealed that the normal-distribution-shaped Josephson tunnel junctions show an exponential decay and no side lobes of the Josephson current as the external magnetic field is increased. This behavior was confirmed experimentally by using the Nb/AlOx/Nb tunnel junctions with a Josephson critical current density of Jc=50 A/cm2, and an area of 10 000 μm2 corresponding to the “small” junction region. Normal-distribution junctions should have a potential for wide applications to photon detection since the external magnetic field to suppress the Josephson current can be lowered to less than one tenth that of other junctions reported.

Time evolution of hydrogen coverage on a well defined tungsten surface detected by the nuclear reaction is discussed. A difference equation is proposed to describe a competition between the adsorption and desorption processes. Overshoot and oscillalion behaviors in the time variation of the hydrogen coverage are explained. A quantitative agreement between the experimental and theoretical results is observed.

Structures, energetics, vibrations, and thermodynamics of the title species were evaluated within the AM1 semiempirical method. Whereas this method also indicates that C 70 ( D 5 h ) is the more abundant component of an equilibrium gas-phase mixture than the C 60 ( I h ) cluster, the possible effect of pressure on the relative stability of C 60 vs C 70 species was pointed out. A comparison with MMP2 and MNDO results is also made.

The isomers of tricyclic hydrocarbons CnH2n−4 having neither side chains nor multiple bonds have been classified into 12 classes from a graph theoretical point of view. We have also found an algorithm for deriving all the structures and the numbers of the isomers, and as an example, we show all the skeletons and the indices of the isomers in the class for C10H16 to which Adamantane belongs.