Modern Physics Letters A

By utilizing the logarithmic transformation and symbolic computation with ansatz functions technique, rational solution and multi-waves interaction solutions are obtained for complex Ginzburg–Landau equation with Kerr law of nonlinearity. Meanwhile, the interaction between rational solutions and the kink wave is also investigated. The dynamics of these obtained solutions are analyzed and described in figures by selecting appropriate values of parameters. Through graphical interpretation, we observe the dynamics and characteristics of lump-kink interaction, soliton–soliton interaction, multi-waves interactions and breathers.

We use the Tridiagonal Representation Approach (TRA) to obtain exact scattering and bound states solutions of the Schrödinger equation for short-range inverse-square singular hyperbolic potentials. The solutions are series of square integrable functions written in terms of the Jacobi polynomial with the Wilson polynomial as expansion coefficients. The series is finite for the discrete bound states and infinite but bounded for the continuum scattering states.

Recently, a physical basis for the Ermakov–Lewis invariant has been pointed out by Padmanabhan [Mod. Phys. Lett. A 33, 1830005 (2018)] and the most general form of the equations admitting such an invariant has been identified. Further generalizations to other equations beyond the Ermakov–Lewis system are derived by considering a more general form of a nonlocal transformation of the Sundman type and the corresponding invariants are derived. Reductions to the time-dependent isotonic oscillator are also obtained.

Image retrieval based on content not only relies heavily upon the type of descriptors, but on the steps taken further. This has been an extensively utilized methodology for finding and fetching out images from the big database of images. Nowadays, a number of methodologies have been organized to increase the CBIR performance. This has an ability to recover pictures relying upon their graphical information. In the proposed method, Neuro-Fuzzy classifier and Deep Neural Network classifier are used to classify the pictures from a given dataset. The proposed approach obtained the highest accuracy in terms of Precision, Recall, and F-measure. To show the efficiency and effectiveness of proposed approach, statistical testing is used in terms of standard deviation, skewness, and kurtosis. The results reveal that the proposed algorithm outperforms other approaches using low computational efforts.

In this paper, we discussed the Schrödinger equation in the presence of the harmonic two electrons interaction for the parabolic quantum dot and the energy spectrum by an analytical method is obtained, then the effective Boltzmann factor in a deformed formalism for modified Dirac delta and uniform distributions are derived. We make use of the superstatistics for the two distributions in physics and the thermodynamic properties of the system are calculated. Ordinary results are recovered for the vanishing deformed parameter. Furthermore, the effect of all parameters in the problems are calculated and shown graphically.

In this paper, we discuss the energy–momentum conservation principle for two-particle system in the case of canonically and Lie-algebraically twist-deformed Galilei Hopf algebra. Particularly, we provide consistency with the coproducts energy and momentum addition law as well as its symmetric with respect to the exchange of particles counterpart. Besides, we show that the vanishing of total four momentum for two Lie-algebraically deformed kinematical models leads to the discrete values of energies and momenta only in the case of the symmetrized addition rules.

The purpose of this paper is to discuss the perfect fluid gravitational collapse in modified f(R) metric gravity theories with non-minimal curvature coupled to matter. For this inference, we investigate the effects on self-gravitating implosion with spherically symmetric non-static geometry in the presence of extra force $[1+\lambda f_2(R)]L_m$, that express the cosmic expansion with dark source constraints. Matching conditions are given in which we have taken the insertion of non-static interior and static exterior regions along with cosmological constant. We have investigated the apparent horizons with effective results and along with their physical interpretation. It is analyzed that the extra component of dark source material reduces the gravitating implosion, hence slowing the rate of collapse. This study also reflects the contribution towards the perfect fluid for the generalization in f(R) gravity with zero coupling constant $\lambda$.

We obtain the geodesics for the simplest possible stealth defect which has a flat spacetime. We, then, discuss the lensing properties of such a defect, and the corresponding image formation. Similar lensing properties can be expected to hold for curved-spacetime stealth defects.

In this paper, Zakharov–Kuznetsov equation is investigated for exact solutions and conservation laws. The well-known Zakharov–Kuznetsov equation contains third-order dispersion, so its validity is restricted to the waves of small amplitudes only. When the amplitude of the wave increases, the velocity and the width of the soliton deviate from the prediction of this equation. To overcome this deficiency, higher-order dispersion term is added to the Zakharov–Kuznetsov equation. We obtain Lie point symmetries and conservation laws for this new model. Wave transformation is applied to convert the nonlinear partial differential equation into another nonlinear ordinary differential equation. Then exact solutions are computed for this with sine–cosine method and modified Kudryashov methods. Obtained solutions are new and are of significant importance in the field of plasma physics.