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The purpose of this paper is to discuss the integrability studies to the long-short wave equation that is studied in the context of shallow water waves. There are several integration tools that are applied to obtain the soliton and other solutions to the equation. The integration techniques are traveling waves, exp-function method, G′/G-expansion method and several others.

The design of the paper is structured with an introduction to the model. First the traveling wave hypothesis approach leads to the waves of permanent form. This eventually leads to the formulation of other approaches that conforms to the expected results.

The findings are a spectrum of solutions that lead to the clearer understanding of the physical phenomena of long-short waves. There are several constraint conditions that fall out naturally from the solutions. These poses the restrictions for the existence of the soliton solutions.

The results are new and are sharp with Lie symmetry analysis and other advanced integration techniques in place. These lead to the connection between these integration approaches.

The propagation of free vibrations in microstretch thermoelastic homogeneous isotropic, thermally conducting plate bordered with layers of inviscid liquid on both sides subjected to stress free thermally insulated and isothermal conditions is investigated in the context of Lord and Shulman (L‐S) and Green and Lindsay (G‐L) theories of thermoelasticity. The secular equations for symmetric and skewsymmetric wave mode propagation are derived. The regions of secular equations are obtained and short wavelength waves of the secular equations are also discussed. At short wavelength limits, the secular equations reduce to Rayleigh surface wave frequency equations. Finally, the numerical solution is carried out for magnesium crystal composite material plate bordered with water. The dispersion curves for symmetric and skew‐symmetric wave modes are computed numerically and presented graphically.

The purpose of this paper is to study the wave propagation in a generalized piezothermoelastic rotating bar of circular cross-section using three-dimensional linear theory of elasticity.

A mathematical model is developed to study the wave propagation in a generalized piezothermelastic rotating bar of circular cross-section by using Lord-Shulman (LS) and Green-Lindsay (GL) theory of thermoelasticity. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been derived by using the thermally insulated/isothermal and electrically shorted/charge free boundary conditions prevailing at the surface of the circular cross-sectional bar. The roots of the frequency equation are obtained by using the secant method, applicable for complex roots.

In order to include the time requirement for the acceleration of the heat flow and the coupling between the temperature and strain fields, the analytical terms have been derived for the non-classical thermo-elastic theories, LS and GL theory. The computed physical quantities such as thermo-mechanical coupling, electro-mechanical coupling, frequency shift, specific loss and frequency have been presented in the form of dispersion curves. From the graphical patterns of the structure, the effect of thermal relaxation times and the rotational speed as well as the anisotropy of the of the material on the various considered wave characteristics is more significant and dominant in the flexural modes of vibration. The effect of such physical quantities provides the foundation for the construction of temperature sensors, acoustic sensor and rotating gyroscope.

In this paper, the influence of thermal relaxation times and rotational speed on the wave number with thermo-mechanical coupling, electro-mechanical coupling, frequency shift, specific loss and frequency has been observed and are presented as dispersion curves. The effect of thermal relaxation time and rotational speed on wave number for the case of generalized piezothermoelastic material of circular cross-section was never reported in the literature. These results are new and original.

The propagation of circular crested waves in a fluid saturated incompressible porous plate is analyzed. The frequency equations, for symmetric and anti‐symmetric waves, connecting the phase velocity with wave number are derived. At short wave length limits the frequency equations for symmetric and antisymmetric waves in a stress free plate reduce to Rayleigh type surface wave frequency equation and the finite thickness plate appears as a semi‐infinite medium. The results at various steps are compared with the corresponding results of classical theory and finally the variations of phase velocity, attenuation coefficient with wave number and displacements amplitudes with distance from the boundary of the plate is presented graphically and discussed.

The purpose of this paper is to study the homoclinic breather waves, rogue waves and multi-soliton waves of the (2 + 1)-dimensional Mel’nikov equation, which describes an interaction of long waves with short wave packets.

The author applies the Hirota’s bilinear method, extended homoclinic test approach and parameter limit method to construct the homoclinic breather waves and rogue waves of the (2 + 1)-dimensional Mel’nikov equation. Moreover, multi-soliton waves are constructed by using the three-wave method.

The results imply that the (2 + 1)-dimensional Mel’nikov equation has breather waves, rogue waves and multi-soliton waves. Moreover, the dynamic properties of such solutions are displayed vividly by figures.

This paper presents efficient methods to find breather waves, rogue waves and multi-soliton waves for nonlinear evolution equations.

The outcome suggests that the extreme behavior of the homoclinic breather waves yields the rogue waves. Moreover, the multi-soliton waves are constructed, including the new breather two-solitary and two-soliton solutions. Meanwhile, the dynamics of these solutions will greatly enrich the diversity of the dynamics of the (2 + 1)-dimensional Mel’nikov equation.

This article describes the background to the widespread application of infrared radiation as a curing technique for paints and coatings, from its origins in the 1930s to the present day. It explains the mechanism of infrared and elaborates on some of the developments which have been made in the technology, especially in terms of control and response. The benefits of infra‐red drying and curing are further illustrated by reference to case studies demonstrating infrared in action.

Many scholars have noted that, since at least 1790, U.K. economic fluctuations have seemed to reach major peaks every 7–10 years. Keynes (1936, ch.18) used the elements of his theory to explain non‐periodic economic fluctuations. His explanation of periodic fluctuations, i.e. cycles, appears in Chapter 22 of the General Theory. As is well known, he believed that fluctuations in “animal spirits” (that were often only loosely connected with the cost and the real rate of return on capital) led to oscillations in investment which, combined with the durability of capital goods, caused the duration of modern major cycles; fluctuations in liquidity preference and the propensity to consume played lesser roles. Bowing to Jevons (1964), Keynes also noted that unstable agricultural inventories could have been a source of waves in the early 19th Century when agriculture was relatively more important in the U.K. But Keynes did not demonstrate just how his investment theory implied a definite cycle period, because he did not merge his multiplier with the accelerator principle to provide an endogenous explanation of periodic turning points in output. Consequently, as Hicks (1950, p. l) notes, Keynes did not demonstrate how investment and income could peak every 7–10 years; his was really a theory of nonperiodic waves.

With the drastically changed pattern of the retail food trade in recent years in which the retailer's role has become little more than that of a provider of shelves for commodities, processed, prepared, packed and weighed by manufacturers, the defence afforded by the provisions of Section 113, Food and Drugs Act, 1955 has really come into its own. Nowadays it is undoubtedly the most commonly pleaded statutory defence. Because this pattern of trade would seem to offer scope for the use of the warranty defence (Sect. 115) in food prosecutions it is a little strange that this defence is not used more often.

The purpose of this study is to introduce a novel approach for seam pucker analysis based on wave shape parameters.

In this method the uneven wavy curve along the puckered seam line was put into a deconvolution process and broken into several simple Gaussian curves using residual mathematical analysis method. First puckered samples with five different grades were produced and scanned by laser triangulated technology. After implementation of deconvolution method, the key geometrical parameters of the decomposed waves such as number of waves and their shape parameters like wave's area, amplitude and wave length were extracted. In addition, an objective method was developed and five indexes were introduced.

Analysis showed that there is a high linear relation with high correlation between all pucker indexes and subjective pucker evaluation.

The goal of this research was to analyse the five grades of seam puckered samples and extract the basic structural parameters to solidify the characteristic of each puckered grade, in order to exclude the influence of human perception.

The purpose of this paper is to numerically investigate time-harmonic elastic wave propagation with the analysis of effective wave velocities and attenuation coefficients in a three-dimensional elastic composite consisting of infinite matrix and uniformly distributed soft, low-contrast and absolutely rigid disc-shaped micro-inclusions.

Within the assumptions of longitudinal mode of a propagating wave as well as dilute concentration and parallel orientation of inclusions in an infinite elastic matrix, Foldy’s dispersion relation is applied for introducing a complex and frequency-dependent wavenumber of homogenized structure. Then, the effective wave velocities and attenuation coefficients are directly defined from the real and imaginary parts of wavenumber, respectively. Included there a far-field forward scattering amplitude by a single low-contrast inclusion given in an analytical form, while for the other types of single scatterers it is determined from the numerical solution of boundary integral equations relative to the displacement jumps across the surfaces of soft inclusion and the stress jumps across the surfaces of rigid inclusion.

On the frequency dependencies, characteristic extremes of the effective wave velocities and attenuation coefficients are revealed and analyzed for different combinations of the filling ratios of involved types of inclusions. Anisotropic dynamic behavior of composite is demonstrated by the consideration of wave propagation in perpendicular and tangential directions relatively to the plane of inclusions. Specific frequencies are revealed for the first case of wave propagation, at which inclusion rigidities do not affect the effective wave parameters.

This paper develops a micromechanical study that provides a deeper understanding of the effect of thin-walled inclusions of diversified rigidities on elastic wave propagation in a three-dimensional composite. Described wave dispersion and attenuation regularities are important for the non-destructive testing of composite materials by ultrasonics.