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We investigate the physics informed neural network method, a deep learning approach, to approximate soliton solution of the nonlinear Schr\"odinger equation with parity time symmetric potentials. We consider three different parity time symmetric potentials, namely Gaussian, periodic and Rosen-Morse potentials. We use physics informed neural network to solve the considered nonlinear partial differential equation with the above three potentials. We compare the predicted result with actual result and analyze the ability of deep learning in solving the considered partial differential equation. We check the ability of deep learning in approximating the soliton solution by taking squared error between real and predicted values. {Further, we examine the factors that affect the performance of the considered deep learning method with different activation functions, namely ReLU, sigmoid and tanh. We also use a new activation function, namely sech which is not used in the field of deep learning and analyze whether this new activation function is suitable for the prediction of soliton solution of nonlinear Schr\"odinger equation for the aforementioned parity time symmetric potentials. In addition to the above, we present how the network's structure and the size of the training data influence the performance of the physics informed neural network. Our results show that the constructed deep learning model successfully approximates the soliton solution of the considered equation with high accuracy., Comment: To appear in Chaos

With the assistance of one fold Darboux transformation formula, we derive rogue wave solutions of the complex modified Korteweg-de Vries equation on an elliptic function background. We employ an algebraic method to find the necessary squared eigenfunctions and eigenvalues. To begin we construct the elliptic function background. Then, on top of this background, we create a rogue wave. We demonstrate the outcome for three distinct elliptic modulus values. We find that when we increase the modulus value the amplitude of rogue waves on the dn-periodic background decreases whereas it increases in the case of cn-periodic background., Comment: 17 pages, 5 figures and Accepted for Publication in Physica Scripta Journal (2021)

We construct soliton solution of a variable coefficients nonlinear Schr\"odinger equation in the presence of parity reflection - time reversal $(\mathcal{PT})-$ symmetric Rosen-Morse potential using similarity transformation technique. We transform the variable coefficients nonlinear Schr\"odinger equation into the nonlinear Schr\"odinger equation with $\mathcal{PT}-$symmetric potential with certain integrability conditions. We investigate in-detail the features of the obtained soliton solutions with two different forms of dispersion parameters. Further, we analyze the nonlinear tunneling effect of soliton profiles by considering two different forms of nonlinear barrier/well and dispersion barrier/well. Our results show that the soliton can tunnel through nonlinear barrier/well and dispersion barrier/well with enlarged and suppressed amplitudes depending on the sign of the height. Our theoretical findings are experimentally realizable and might help to model the optical devices., Comment: 11 pages, 8 figures and Accepted for publication in The European Physical Journal B (2021)

We construct rogue wave solutions of a fifth-order nonlinear Schr\"odinger equation on the Jacobian elliptic function background. By combining Darboux transformation and the nonlinearization of spectral problem, we generate rogue wave solution on two different periodic wave backgrounds. We analyze the obtained solutions for different values of system parameter and point out certain novel features of our results. We also compute instability growth rate of both $dn$ and $cn$ periodic background waves for the considered system through spectral stability problem. We show that instability growth rate decreases (increases) for $dn$-$(cn)$ periodic waves when we vary the value of the elliptic modulus parameter., Comment: 26 pages, 7 figures and published in Physics Letters A journal

We construct rogue wave solutions on the double periodic background for the Hirota equation through one fold Darboux transformation formula. We consider two types of double periodic solutions as seed solutions. We identify the squared eigenfunctions and eigenvalues that appear in the one fold Darboux transformation formula through an algebraic method with two eigenvalues. We then construct the desired solution in two steps. In the first step, we create double periodic waves as the background. In the second step, we build rogue wave solution on the top of this double periodic solution. We present the localized structures for two different values of the arbitrary parameter each one with two different sets of eigenvalues., Comment: 9 pages, 7 figures and accepted for publication in The European Physical Journal Plus Journal

We investigate the existence and stability of dissipative soliton solution in a system described by complex Ginzburg-Landau (CGL) equation with asymmetric complex potential, which is obtained from original parity reflection - time reversal ($\mathcal{PT}$) symmetric Rosen-Morse potential. In this study, stability of solution is examined by numerical analysis to show that solitons are stable for some parameter ranges for both self-focusing and self-defocusing nonlinear modes. Dynamical properties such as evolution and transverse energy flow for both modes are also analyzed. Obtained results are useful for experimental designs and applications in related fields., Comment: 15 pages, 10 figures. To be published in Physics Letters A journal. arXiv admin note: substantial text overlap with arXiv:1812.10343

We provide the first experimental confirmation of a three-way quantum coherence identity possessed by single pure-state photons. Our experimental results demonstrate that traditional wave-particle duality is specifically limited by this identity. As a new consequence, we show that quantum duality itself can be amplified, attenuated, or turned completely off. In the Young double-slit context this quantum coherence identity is found to be directly relevant, and it supplies a rare quantitative backup for one of Bohr's philosophical pronouncements., Comment: 5 pages, 5 figures

We investigate the existence of stable soliton solution in a system described by complex Ginzburg-Landau (CGL) equation with near parity reflection - time reversal ($\mathcal{PT}$) symmetric Rosen-Morse potential. In this study, the stability of solution is examined by numerical analysis to show that solitons are stable for some parameter ranges. The dynamical properties such as evolution and transverse energy flow for both self-focusing and self-defocusing nonlinear mode are also analyzed. The obtained results are useful for experimental designs and applications in related fields., Comment: 7 pages, 11 figures

The hand gestures are one of the typical methods used in sign language. It is very difficult for the hearing-impaired people to communicate with the world. This project presents a solution that will not only automatically recognize the hand gestures but will also convert it into speech and text output so that impaired person can easily communicate with normal people. A camera attached to computer will capture images of hand and the contour feature extraction is used to recognize the hand gestures of the person. Based on the recognized gestures, the recorded soundtrack will be played., Comment: 5 pages, 5 figures, International Conference on Innovations and Discoveries in Science, Engineering and Technology(ICIDSET) 2018

We report on synthesis and characterization of gallide cluster based Mo8Ga41 superconductor. Transport and magnetization measurements confirm the superconducting transition temperature to be 9.8 K. The upper critical field, lower critical field, Ginzburg-Landau coherence length and penetration depth are estimated to be 11.8T, 150G, 5.2nm, 148nm respectively. The electronic band structure, density of states and phonon dispersion curve calculations are obtained by using Density Functional Theory. The core level X-ray Photoelectron Spectroscopy (XPS) reveals the binding energy information of the constituting elements Mo and Ga in Mo8Ga41. The valence band spectra from XPS is in good agreement with calculated density of states (DOS). The zero field critical current density (Jc) at T = 2 K is ~ 3*10^5 A/cm^2 which is indicative of efficient flux pinning in the as grown compound. About two fold enhancement in critical current density with application of external pressure (1.1 GPa) is observed with marginal decrease in transition temperature. The fitting of current density to double exponential model confirms possibility of two gap superconductivity in Mo8Ga41.

SrxBi2Se3 is recently reported to be a superconductor derived from topological insulator Bi2Se3. It shows a maximum resistive Tc of 3.25 K at ambient pressure. We report magnetic (upto 1 GPa) and transport properties (upro 8 Gpa) under pressure for single crystalline Sr0.1Bi2Se3 superconductor. Magnetic measurements show that Tc decreases from ~2.6 K (0 GPa) to ~1.9 K (0.81 GPa). Similar behavior is observed in transport properties as well without much change in the metallic characteristics in normal state resistivity. No reentrant superconducting phase (Physical Review B 93, 144514 (2016)) is observed at high pressure. Normal state resistivity near Tc is explained by Fermi liquid model. Above 100 K, a polaronic hopping conduction mechanism with two parallel channels for current flow is indicated. Band structure calculations indicate decreasing density of states at Fermi level with pressure. In consonance with transition temperature suppression in conventional BCS low Tc superconductors, the pressure effect in SrxBi2Se3 is well accounted by pressure induced band broadening.

We construct vector rogue wave solutions of the two-dimensional two coupled nonlinear Schr\"{o}dinger equations with distributed coefficients, namely diffraction, nonlinearity and gain parameters through similarity transformation technique. We transform the two-dimensional two coupled variable coefficients nonlinear Schr\"{o}dinger equations into Manakov equation with a constraint that connects diffraction and gain parameters with nonlinearity parameter. We investigate the characteristics of the constructed vector rogue wave solutions with four different forms of diffraction parameters. We report some interesting patterns that occur in the rogue wave structures. Further, we construct vector dark rogue wave solutions of the two-dimensional two coupled nonlinear Schr\"{o}dinger equations with distributed coefficients and report some novel characteristics that we observe in the vector dark rogue wave solutions., Comment: Accepted for publication in The European Physical Journal B

We construct spatiotemporal localized envelope solutions of a (3+1)-dimensional nonlinear Schr\"{o}dinger equation with varying coefficients such as dispersion, nonlinearity and gain parameters through similarity transformation technique. The obtained localized rational solutions can serve as prototypes of rogue waves in different branches of science. We investigate the characteristics of constructed localized solutions in detail when it propagates through six different dispersion profiles, namely constant, linear, Gaussian, hyperbolic, logarithm and exponential. We also obtain expressions for the hump and valleys of rogue wave intensity profiles for these six dispersion profiles and study the trajectory of it in each case. Further, we analyze how the intensity of another localized solution, namely breather, changes when it propagates through the aforementioned six dispersion profiles. Our studies reveal that these localized solutions co-exist with the collapsing solutions which are already found in the (3+1)-dimensional nonlinear Schr\"{o}dinger equation. The obtained results will help to understand the corresponding localized wave phenomena in related fields., Comment: 32 pages, 17 figures, Accepted for publication in Chaos

We construct rogue wave and breather solutions of a quasi-two-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap. We show that the trapping potential and an arbitrary functional parameter that present in the similarity transformation should satisfy a constraint for the considered equation to be integrable and yield the desired solutions. We consider two different forms of functional parameters and investigate how the density of the rogue wave and breather profiles vary with respect to these functional parameters. We also construct vector localized solutions of a two coupled quasi-two-dimensional Bose-Einstein condensate system. We then investigate how the vector localized density profiles modify in the constant density background with respect to the functional parameters. Our results may help to manipulate matter rogue waves experimentally in the two-dimensional Bose-Einstein condensate systems., Comment: 16 pages, Published in Eur. Phys. J. B

We analyze vector localized solutions of two-component Bose-Einstein condensates (BECs) with variable nonlinearity parameter and external trap potential through similarity transformation technique which transforms the two coupled Gross-Pitaevskii equations into a pair of coupled nonlinear Schr\"{o}dinger equations with constant coefficients under a specific integrability condition. In this analysis we consider three different types of external trap potentials: a time-independent trap, a time-dependent monotonic trap, and a time-dependent periodic trap. We point out the existence of different interesting localized structures, namely rogue waves, dark-and bright soliton-rogue wave, and rogue wave-breather-like wave for the above three cases of trap potentials. We show how the vector localized density profiles in a constant background get deformed when we tune the strength of the trap parameter. Further we investigate the nature of the trajectories of the nonautonomous rogue waves. We also construct the dark-dark rogue wave solution for repulsive-repulsive interaction of two-component BECs and analyze the associated characteristics for the three different kinds of traps. We then deduce single, two and three composite rogue waves for three component BECs and discuss the correlated characteristics when we tune the strength of the trap parameter for different trap potentials., Comment: 18 pages, Accepted for publication in Phys. Rev. E

Critical current density (Jc), thermal activation energy (U0), and upper critical field (Hc2) of La1-xSmxO0.5F0.5BiS2 (x = 0.2, 0.8) superconductors are investigated from magnetic field dependent \r{ho}(T) studies. The estimated upper critical field (Hc2) has low values of 1.04 T for x = 0.2 and 1.41 T for x = 0.8. These values are lower than Sm free LaO0.5F0.5BiS2 superconductor (1.9 T). The critical current density (Jc) is estimated to be 1.35*105 A/cm2 and 5.07 *105 A/cm2 (2 K) for x = 0.2 and 0.8 respectively, using the Bean's model. The thermal activation energy (U0/kB) is 61 K for x = 0.2 and 140 K for x =0.8 as calculated from Arrhenius plots at low magnetic field (1 T) and indicates a strong flux pinning potential which might be co-existing with applied magnetic field., Comment: 13 pages, 4 figures

We have investigated the pressure effect on the newly discovered samarium doped La1-xSmxO0.5F0.5BiS2 superconductors. More than threefold increase in Tc (10.3 K) is observed with external pressure (at ~1.74 GPa at a rate of 4.08 K/GPa)) for x = 0.2 composition. There is a concomitant large improvement in the quality of the superconducting transition. Beyond this pressure Tc decreases monotonously at the rate of -2.09 K/GPa. In the x = 0.8 sample, we do not observe any enhancement in Tc with application of pressure (up to 1.76 GPa). The semiconducting behavior observed in the normal state resistivity of both of the samples is significantly subdued with the application of pressure which, if interpreted invoking thermal activation process, implies that the activation energy gap of the carriers is significantly reduced with pressure. We believe these observations should generate further interest in the La1-xSmxO0.5F0.5BiS2 superconductors., Comment: 17 pages, 5 figures

We construct breather and rogue wave solutions of a variable coefficient nonlinear Schr\"odinger equation with an external linear potential. This generalized model describes the nonlinear wave propagation in an inhomogeneous plasma/medium. We derive several localized solutions including Ma breather, Akhmediev breather, two-breather and rogue wave solutions of this model and show how the inhomogeneity of space modifies the shape and orientation of these localized structures. We also depict the trajectories of the inhomogeneous rogue wave. Our results may be useful for controlling plasmonic energy along the plasma surface., Comment: 15 pages, 11 figures, submitted for publication. arXiv admin note: text overlap with arXiv:1407.2701

We construct higher order rogue wave solutions and breather profiles for the quasi-one-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap through the similarity transformation technique. We consider three different forms of traps, namely (i) time-independent expulsive trap, (ii) time-dependent monotonous trap and (iii) time-dependent periodic trap. Our results show that when we change a parameter appearing in the time-independent or time-dependent trap the second and third-order rogue waves transform into the first-order like rogue waves. We also analyze the density profiles of breather solutions. Here also we show that the shapes of the breathers change when we tune the strength of trap parameter. Our results may help to manage rogue waves experimentally in a BEC system., Comment: 17 pages, 17 figures, revised version, accepted for publication in Phys. Rev. E

We construct exact solutions for a system of two nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the $\big(\frac{G'}{G}\big)$ expansion method, we derive exact solutions to this model for two different wave speeds. For each wave velocity we report three different forms of solutions. We also discuss the biological relevance of the solutions obtained., Comment: Accepted for Publication in Commun. Nonlin. Sci. Num. Sim. (2012)