Current Issue : October - December Volume : 2019 Issue Number : 4 Articles : 5 Articles
The study of physical systems endowed with a position-dependent\nmass (PDM) remains a fundamental issue of quantum mechanics.\nIn this paper we use a new approach, recently developed by us\nfor building the quantum kinetic energy operator (KEO) within\nthe Schrodinger equation, in order to construct a new class of exactly\nsolvable models with a position varying mass, presenting a\nharmonic-oscillator-like spectrum. To do so we utilize the formalism\nof supersymmetric quantum mechanics (SUSY QM) along with\nthe shape invariance condition. Recent outcomes of non-Hermitian\nquantum mechanics are also taken into account....
The Sawada-Kotera equation with a nonvanishing boundary condition, which models the evolution of steeper waves of shorter\nwavelength than those depicted by the Korteweg de Vries equation, is analyzed and also the perturbed Korteweg de Vries (pKdV)\nequation. For this goal, a capable method known as the multiple exp-function scheme (MEFS) is formally utilized to derive the\nmultiple soliton solutions of the models.The MEFS as a generalization of Hirotaâ??s perturbation method actually suggests a systematic\ntechnique to handle nonlinear evolution equations (NLEEs)....
About a century ago, the French artillery commandant Charbonnier envisioned an intriguing result on the trajectory of a projectile\nthat is moving under the forces of gravity and air resistance. In 2000, Groetsch discovered a significant gap in Charbonnierâ??s work\nand provided a valid argument for a certain special case. The goal of the present article is to establish a rigorous new approach to\nthe full result. For this, we develop a theory of those functions which can be sandwiched, in a natural way, by a pair of quadratic\npolynomials. It turns out that the convexity or concavity of the derivative plays a decisive role in this context....
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The unsteady magnetohydrodynamics (MHD) flow of nanofluid with variable fluid properties over an inclined stretching sheet\nin the presence of thermal radiation and chemical reaction is studied taking into account the effect of variable fluid properties\nin thermal conductivity and diffusion coefficient. The governing partial differential equations are transformed into ordinary\ndifferential equations by using similarity transformation. The numerical solutions of the problem are obtained by using the fourth\norder Runge-Kutta method in line with the shooting technique. It is found that the increase in both thermal conductivity and\nradiative heat flux decreases the heat transfer rate but increases the skin friction and mass transfer rates. It is further observed that\nthe increase in porosity parameter and magnetic field reduces the skin friction, heat, and mass transfer rates....
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