In this paper, starting from the careful analysis on the characteristics of the Burgers equation and the KdV equation as well as the KdV-Burgers equation, the superposition method is put forward for constructing the solitary wave solutions of the KdV-Burgers equation from those of the Burgers equation and the KdV equation. The solitary wave solutions for the KdV-Burgers equation are presented successfully by means of this method.

In a recent paper (Tranet al, Ann. Phys.311, 204 (2004)), some asymptotic number theoretical results on the partitioning of an integer were derived exploiting its connection to the quantum density of states of a many-particle system. We generalise these results to obtain an asymptotic formula for therestricted or coloured partitionsp_k^s(n), which is the number of partitions of an integern into the summand of sth powers of integers such that each power of a given integer may occur utmostk times. While the method is not rigorous, it reproduces the well-known asymptotic results fors = 1 apart from yielding more general results for arbitrary values ofs.

Elastic scattering of 800 MeV/c pions by¹²C has been studied in the diffraction model with a view to determine pion optical potential by the method of inversion. Finding an earlier diffraction model analysis to be deficient in some respects, we propose a Glauber model based parametrization for the elasticS-matrix and show that it provides an exceedingly good fit to the pion-carbon data. The proposed elasticS-matrix gives a closed expression for the pion-¹²C optical potential by the method of inversion in the high energy approximation.

Langevin approach implemented in the inelastic cross-sections measured for the low-energy electrons colliding with metallic clusters points out that statical form of the polarizability dominate at energies less than 1.25 eV. The dynamical form comes into play at energies around 1.3 eV. The form of the polarizabilities indicates that polarizability of the metallic clusters is energy-dependent.

In this work, the inhomogeneous equation of heat conduction was exactly solved by applying inhomogeneous boundary conditions for laser crystals of aspect ratio=1 (aspect ratio=radius of the laser rod/length of the laser rod). We have shown that the paraxial ray approximation leads the solution to be a function ofr², that is, the approximation is equivalent to a situation in which a homogeneous pump source is used. The solution was then used to derive expressions for the overall phase shift, focal length of the thermal lens and the end effect induced curvature of the end face. The expressions were then applied to Nd:YAG laser medium. The result shows a meaningful correction of the order of 0.001 cm to the focal length of Nd:YAG rod for 3 W source power and beam waist of 100 μm.

Dynamic holography in photorefractive materials using self-pumped phase conjugate beam of the object beam itself as the other writing beam is proposed. Our detailed theoretical analysis shows four-fold increase in the diffraction efficiency of dynamic holograms if recorded using this geometry even in photorefractive crystal like BTO (having low optical activity) without applying external field. Detailed theoretical analysis is given.

Two designs of long-wavelength band erbium-doped fiber amplifier (L-band EDFA) for gain clamping in double-pass systems are demonstrated and compared. The first design is based on ring laser technique where a backward amplified spontaneous emission (ASE) from the second stage is routed into the feedback loop to create an oscillating laser for gain clamping. The gain is clamped at 18.6 d B from -40 to -80 dBm with a gain variation of less than ±0.1 dB and a noise figure of less than 6 dB. Another scheme is based on partial reflection of ASE into the EDFA, which is demonstrated using a narrowband fiber Bragg grating. This scheme achieves a good gain clamping characteristic up to -12 dBm of input signal power with a gain variation of less than ±0.3 dB from a clamped gain of 22 dB. The noise figure of a 1580 nm signal is maintained below 5 dB in this amplifier since this scheme is not based on lasing mechanism. The latter scheme is also expected to be free from the relaxation oscillation problem.

A theoretical study is made on the generation mechanism of ion acoustics wave in the presence of lower hybrid wave turbulence field in inhomogeneous plasma on the basis of plasma-maser interaction. The lower hybrid wave turbulence field is taken as the low-frequency turbulence field. The growth rate of test high frequency ion acoustics wave is obtained with the involvement of spatial density gradient parameter. A comparative study of the role of density gradient for the generation of ion acoustics wave on the basis of plasma-maser effect is presented. It is found that the density gradient influences the growth rate of ion acoustics wave.

Adhesion of zein to solid substrates has been studied using surface energy profiles as indices and by adhesion mapping using atomic force microscopy (AFM). Different plasticizers like glycerol and sorbitol have been used to form mixed films with zein and properties of these films are studied using surface energy profiles. Comparison of the results from the different mixed samples with those from the pure zein films showed that force mapping could identify areas rich in protein. The adhesion maps produced were deconvoluted from sample topography and contrasted with the data obtained from contact angle measurements. A comparison of the two methods shows that the extent of contact angle hysteresis is indicative of both hydrophobicity of the surface as well as the force of adhesion. Mechanical properties and microstructure of zein films prepared by casting from solutions and using Langmuir-Blodgett film technique have been investigated. Pure zein seemed brittle and exhibited an essentially linear relationship between stress and strain. Films with plasticizer were tougher than these films. In general, mixed films showed better mechanical properties than pure films and had higher ultimate tensile strength and increased per cent elongation. Further, the mixed films of zein showed a higher force of adhesion compared to the pure films.

It is shown that it is possible to bosonize fermions in any number of dimensions using the hydrodynamic variables, namely the velocity potential and density. The slow part of the Fermi field is defined irrespective of dimensionality and the commutators of this field with currents and densities are exponentiated using the velocity potential as conjugate to the density. An action in terms of these canonical bosonic variables is proposed that reproduces the correct current and density correlations. This formalism in one dimension is shown to be equivalent to the Tomonaga-Luttinger approach as it leads to the same propagator and exponents. We compute the one-particle properties of a spinless homogeneous Fermi system in two spatial dimensions with long-range gauge interactions and highlight the metal-insulator transition in the system. A general formula for the generating function of density correlations is derived that is valid beyond the random phase approximation. Finally, we write down a formula for the annihilation operator in momentum space directly in terms of number conserving products of Fermi fields.

The exact formula of T_c’s equation and the isotope effect exponent of two-band s-wave superconductors in the weak-coupling limit are derived by considering the influence of interband interaction. In each band, our model consists of two pairing interactions: the electron-phonon interaction and non-electron-phonon interaction. We find that the isotope effect exponent of MgB₂, α = 0.3 with T_c ≈ 40 K can be found in the weak coupling regime and interband interaction of electron-phonon shows more effect on the isotope effect exponent than on the interband interaction of non-phonon.

AlO molecule was excited in a DC arc in air running between two aluminium electrodes. Rotational structure of the (0,0) band of the B²Σ⁺-X²Σ⁺ system of AlO molecule was photographed in the first order of a 10.6 m concave grating spectrograph. Intensity distribution amongst the well-resolved rotational lines of R₁ and R₂ branches was recorded and the average rotational temperature calculated from these has been determined as 2880 ± 100 K.

A general method is used for the construction of second constant of motion of fourth order in momenta using the complex coordinates (z,_z^-). A fourth-order potential equation is obtained whose solutions directly provide a large class of integrable systems. The potential equation is tested with an interesting example which admits second constants of motion.

Einstein field equations for static anisotropic spheres are solved and exact interior solutions obtained. This paper extends earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities. Two classes of solutions are possible. The first class contains the limiting caseμ,∝ r^-2 for the energy density which arises in many astrophysical applications. In the second class the singularity at the centre of the star is not present in the energy density.

Two fully quantized generalized Jaynes-Cummings models for the interaction of a two-level atom with radiation field are treated, one involving intensity dependent coupling and the other involving multiphoton interaction between the field and the atom. The unitary transformation method presented here not only solves the time dependent problem but also allows a determination of the eigensolutions of the interacting Hamiltonian at the same time.