Results Phys. 51, 106624 (2023) and 50, 106566 (2023) have recently made some outstanding contributions to the studies of certain Korteweg-de Vries (KdV)-type systems. Inspired by those ...contributions, around a noncharacteristic movable singular manifold, this Letter works out two sets of the auto-Bäcklund transformations for an enlarged three-coupled KdV system, along with some solitons. All of our results rely on the coefficients in that system.
Cosmic plasmas are considered as the most abundant form of ordinary matter in the Universe while observations of the cosmic dust in different regions provide an insight into the Universe's recycling ...processes. For different types of the cosmic dusty plasmas, we hereby, with the symbolic computation and observational/experimental supports, study a (3+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili-Burgers-type equation, which can describe the electron-acoustic, dust-acoustic, positron-acoustic, dust-magneto-acoustic, ion-acoustic, magneto-acoustic, ion, quantum-dust-ion-acoustic or dust-ion-acoustic waves in one of the cosmic/laboratory dusty plasmas. With respect to the fluctuation of the electron or ion density, or perturbation of the magnitude of the magnetic field, or electrostatic wave potential, or radial-direction component of the velocity of ions or dust particles, a set of the auto-Bäcklund transformations, several soliton families and a set of the similarity reductions are symbolically computed out, depending on the variable coefficients which represent the dispersion, nonlinearity, geometric effect, Burgers/dusty-fluid-viscosity dissipation and diffraction/transverse perturbation. Variable-coefficient constraints on the soliton solutions are presented. Our analytic results are in agreement with those dusty-plasma-experimentally reported. Future dusty-plasma experiments and observations might justify some other effects hereby offered.
Recent progress in optical fibers is impressive, while nonlinear Schrödinger-type models are seen in fiber optics and other fields (such as ferromagnetism, plasma physics, Bose–Einstein condensation ...and oceanography). Hereby, our symbolic computation on a three-coupled variable-coefficient nonlinear Schrödinger system is performed, for the picosecond-pulse attenuation/amplification in a multicomponent inhomogeneous optical fiber with diverse polarizations/frequencies. For the slowly-varying envelopes of optical modes, we obtain a similarity reduction, an auto-Bäcklund transformation and some analytic solutions, which rely on the optical-fiber variable coefficients, i.e., the fiber loss/gain, nonlinearity and group velocity dispersion. Relevant variable-coefficient constraints are presented. Our results might be of some use in the construction of logic gates, optical computing, soliton switching, design of fiber directional couplers, quantum information processing, soliton amplification in the wavelength division multiplexing systems, solitonic studies in the all-optical devices and birefringence fiber systems.
In the Solar System, water and water waves are commonly seen: For the Earth, water is “at the core of sustainable development” and “at the heart of adaptation to climate change”; For the Enceladus, ...Cassini spacecraft discovers a possible global ocean of liquid water beneath an icy crust; For the Titan, Cassini spacecraft suggests an icy shell floating atop a global ocean. Shallow water waves near the ocean beaches or in the lakes can be described by the Boussinesq-Burgers-type equations. In this Letter, on the higher-order Boussinesq-Burgers system, symbolic computation helps us to go from the two-dimensional Bell polynomials to construct two non-auto-Bäcklund transformations and to proceed from the Painlevé-Bäcklund format to obtain four auto-Bäcklund transformations with some soliton solutions. All of our results are shown to be dependent on the constant coefficient in the system.
•1. Oceanic water waves are actively studied. Taking into account the nonlinear and dispersive long gravity waves in two horizontal directions on the shallow water of an open sea or a wide channel of ...finite depth. 3. Investigating a generalized (2+1)-dimensional dispersive long-wave system. 4. With symbolic computation while with respect to the horizontal velocity and wave elevation above the undisturbed water surface. 5. working out two non-auto-Backlund transformations and two auto-Backlund transformations with solitons.
Oceanic water waves are actively studied. Hereby, taking into account the nonlinear and dispersive long gravity waves in two horizontal directions on the shallow water of an open sea or a wide channel of finite depth, we investigate a generalized (2+1)-dimensional dispersive long-wave system. With symbolic computation while with respect to the horizontal velocity and wave elevation above the undisturbed water surface, we work out two non-auto-Bäcklund transformations and two auto-Bäcklund transformations with solitons. All of our results are dependent on the constant coefficients in the original system.
Abstract
We present a sample of 135,873 RR Lyrae stars (RRLs) with precise photometric metallicity and distance estimates from our newly calibrated
P
–
ϕ
31
–
R
21
–Fe/H/
P
–
R
21
–Fe/H and
G
-band ...absolute magnitude–metallicity relations. The
P
–
ϕ
31
–
R
21
–Fe/H and
P
–
R
21
–Fe/H relations for type RRab and type RRc stars are obtained from nearly 2700 Gaia-identified RRLs, with precise
ϕ
31
and
R
21
measurements from light curves and metallicity estimates from spectroscopy. Using a few hundreds of nearby RRLs, with accurate distances estimated from the parallax measurements in Gaia Early Data Release 3, new
G
-band absolute magnitude–metallicity relations and near-IR period–absolute magnitude–metallicity relations are constructed. External checks, using other high-resolution spectroscopic samples of field RRLs and RRL members of globular clusters, show that the typical uncertainties in our photometric metallicity estimates are about 0.24 and 0.16 dex for type RRab and type RRc stars, respectively, without significant systematic bias with respect to the high-resolution spectroscopic metallicity measurements. The accuracies of these metallicity estimates are much improved, especially for type RRab stars, when compared to those provided by Gaia Data Release 3. Validations of our distance estimates, again using members of globular clusters, show that the typical distance errors are only 3%–4%. The distance moduli
μ
0
= 18.503 ± 0.001 (stat) ± 0.040 (syst) mag for the Large Magellanic Cloud (LMC) and
μ
0
= 19.030 ± 0.003 (stat) ± 0.043 (syst) mag for the Small Magellanic Cloud (SMC) are estimated from our type RRab star sample and are in excellent agreement with previous measurements. The mean metallicities of the LMC and SMC derived in this work are also consistent with previous determinations. Using our sample, a steep metallicity gradient of −0.024 ± 0.001 dex kpc
−1
is found for the LMC, while a negligible metallicity gradient is obtained for the SMC.
Nowadays, people are interested in many nonlinear models in sciences and engineering, e.g., a (2+1)-dimensional generalized nonlinear evolution system in fluid dynamics, plasma physics, nonlinear ...optics and quantum mechanics. We purpose to study that system by means of constructing one set of the bilinear auto-Bäcklund transformations and one set of the similarity reductions. Our bilinear auto-Bäcklund transformations can link certain solutions for that system with other solutions for that system itself, while our similarity reductions go from that system to a known ordinary differential equation. Our results depend on all the coefficients in that system. The present work could assist the future investigations in fluid dynamics, quantum mechanics, nonlinear optics and plasma physics.
Ahmed et al. (2023) has initiated the readers into a good study of certain homoclinic breathers and rational solitons for a (3+1)-dimensional nonlinear soliton equation in the shallow water. ...Nevertheless, this Letter highlights the existence of a (3+1)-dimensional generalized nonlinear evolution system for the shallow water waves, which fully covers the aforementioned equation. For that generalized system, based on the computerized symbolic computation and singular manifold, this Letter accomplishes an auto-Bäcklund transformation coupled with some solitons beyond the travelling waves. Results are associated with the coefficients in that generalized system.
•Existence of a (3+1)-dimensional generalized nonlinear evolution system for the shallow water waves.•That generalized system fully covering the equation in Ahmed et al. (2023).•Studying that generalized system with symbolic computation and singular manifold.•Accomplishing an auto-Backlund transformation with some solitons beyond the travelling waves.
