Existence and Large Time Behavior of Entropy Solutions to One-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient DampingRead the full article
Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches.
Chief Editor, Prof Di Matteo (Department of Mathematics, King’s College London), engages in world-leading multidisciplinary and data-driven research focussed on the analysis of complex data from the perspective of a statistical physicist.
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Fixed-Point Theorem for Nonlinear -Contraction via -Distance
The aim of this paper is to introduce a notion of -contraction defined on a metric space with -distance. Moreover, fixed-point theorems are given in this framework. As an application, we prove the existence and uniqueness of a solution for the nonlinear Fredholm integral equations. Some illustrative examples are provided to advocate the usability of our results.
Exact Analytical Solutions of Nonlinear Fractional Liouville Equation by Extended Complex Method
The extended complex method is investigated for exact analytical solutions of nonlinear fractional Liouville equation. Based on the work of Yuan et al., the new rational, periodic, and elliptic function solutions have been obtained. By adjusting the arbitrary values to the constants in the constructed solutions, it can describe the physical phenomena to the traveling wave solutions, since traveling wave has significant value in applied sciences and engineering. Our results indicate that the extended complex technique is direct and easily applicable to solve the nonlinear fractional partial differential equations (NLFPDEs).
A Riemann-Hilbert Approach to the Multicomponent Kaup-Newell Equation
A Riemann-Hilbert approach is developed to the multicomponent Kaup-Newell equation. The formula is presented of -soliton solutions through an identity jump matrix related to the inverse scattering problems with reflectionless potential.
An Extended -Metric-Type Space and Related Fixed Point Theorems with an Application to Nonlinear Integral Equations
In this paper, the concept of sequential -metric spaces has been introduced as a generalization of usual metric spaces, -metric spaces and specially of -metric spaces. Several topological properties of such spaces have been discussed here. In view of this notion, we prove fixed point theorems for some classes of contractive mappings over such spaces. Supporting examples have been given in order to examine the validity of the underlying space and in respect to our proven fixed point theorems.
Study of Dust-Acoustic Multisoliton Interactions in Strongly Coupled Dusty Plasmas
The effect of the structure parameter on the compressibility of dust grains and soliton behavior in a dusty plasma system consisting of Maxwellian electrons, ions, and dust grains charged with a negative charge has been studied. In the theoretical study, a reductive perturbation technique was used to derive the Korteweg-de Vries (KdV) equation and employ the Hirota bilinear method to obtain multisoliton solution. It is found that coupling and structure parameters have a clear effect on the compressibility. These changes in the compressibility affected the amplitude and width of interactive solitons, in addition to the phase shifts resulting from the interaction. These results can be used to understand the behavior of solitary waves that occur in various natural and laboratory plasma environments with dust impurity situations.
Long-Range Scalar Forces in Five-Dimensional General Relativity
We present new results regarding the long-range scalar field that emerges from the classical Kaluza unification of general relativity and electromagnetism. The Kaluza framework reproduces known physics exactly when the scalar field goes to one, so we studied perturbations of the scalar field around unity, as is done for gravity in the Newtonian limit of general relativity. A suite of interesting phenomena unknown to the Kaluza literature is revealed: planetary masses are clothed in scalar field, which contributes 25% of the mass-energy of the clothed mass; the scalar potential around a planet is positive, compared with the negative gravitational potential; at laboratory scales, the scalar charge which couples to the scalar field is quadratic in electric charge; a new length scale of physics is encountered for the static scalar field around an electrically-charged mass, ; the scalar charge of elementary particles is proportional to the electric charge, making the scalar force indistinguishable from the atomic electric force. An unduly strong electrogravitic buoyancy force is predicted for electrically-charged objects in the planetary scalar field, and this calculation appears to be the first quantitative falsification of the Kaluza unification. Since the simplest classical field, a long-range scalar field, is expected in nature, and since the Kaluza scalar field is as weak as gravity, we suggest that if there is an error in this calculation, it is likely to be in the magnitude of the coupling to the scalar field, not in the existence or magnitude of the scalar field itself.