scholarly journals Families of Solutions of Multitemporal Nonlinear Schrödinger PDE

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1995
Author(s):  
Cristian Ghiu ◽  
Constantin Udriste ◽  
Lavinia Laura Petrescu
Keyword(s):  
Wave Packet ◽  
Exact Solutions ◽  
Research Group ◽  
Directional Derivative ◽  
Amplitude Equation ◽  
Scaling Analysis ◽  
Nonlinear Schrödinger ◽  
Derivative Term ◽  
New Construction ◽  
First Time

The multitemporal nonlinear Schrödinger PDE (with oblique derivative) was stated for the first time in our research group as a universal amplitude equation which can be derived via a multiple scaling analysis in order to describe slow modulations of the envelope of a spatially and temporarily oscillating wave packet in space and multitime (an equation which governs the dynamics of solitons through meta-materials). Now we exploit some hypotheses in order to find important explicit families of exact solutions in all dimensions for the multitime nonlinear Schrödinger PDE with a multitemporal directional derivative term. Using quite effective methods, we discovered families of ODEs and PDEs whose solutions generate solutions of multitime nonlinear Schrödinger PDE. Each new construction involves a relatively small amount of intermediate calculations.

scholarly journals New Exact Solutions for High Dispersive Cubic-Quintic Nonlinear Schrödinger Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yongan Xie ◽  
Shengqiang Tang
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Bifurcation Theory ◽  
Solitary Wave Solutions ◽  
Nonlinear Schrödinger ◽  
Light Pulses ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
First Time ◽  
Quintic Nonlinear Schrödinger Equation

We study a class of high dispersive cubic-quintic nonlinear Schrödinger equations, which describes the propagation of femtosecond light pulses in a medium that exhibits a parabolic nonlinearity law. Applying bifurcation theory of dynamical systems and the Fan sub-equations method, more types of exact solutions, particularly solitary wave solutions, are obtained for the first time.

Evidence of a predation event on a tagged Mediterranean spearfish (Tetrapturus belone; Pisces, Istiophoridae), inferred from pop-up satellite tagging data

2020 ◽  
Vol 33 ◽  
pp. 23
Author(s):  
Danilo Malara ◽  
Pietro Battaglia ◽  
Pierpaolo Consoli ◽  
Erika Arcadi ◽  
Simonepietro Canese ◽  
...  
Keyword(s):  
Mediterranean Sea ◽  
Research Group ◽  
Marine Mammals ◽  
Biodiversity Hotspot ◽  
Pelagic Species ◽  
Archival Tag ◽  
Abiotic Parameters ◽  
Predation Event ◽  
Satellite Tagging ◽  
First Time

The Strait of Messina is located at the centre of the Mediterranean Sea and is considered a biodiversity hotspot and an obligatory seasonal passage for different pelagic species such as sharks, marine mammals, and billfishes. For the first time, in the Strait of Messina, our research group tagged a Mediterranean spearfish (Tetrapturus belone) using a pop-up satellite archival tag (PSAT). The observation of abiotic parameters (depth, light, and temperature) recorded by the PSAT confirmed that the tagged specimen was predated after about nine hours. The tag was then regurgitated 14 days after the tag deployment date. The analysis of collected data seems to indicate that the predator may be an ectothermic shark, most likely the bluntnose sixgill shark (Hexanchus griseus).

scholarly journals Experimental investigation to characterize simple versus multi scaling analysis of hydraulic conductivity at a mesoscale

2021 ◽  
Author(s):  
Guglielmo Federico Antonio Brunetti ◽  
Samuele De Bartolo ◽  
Carmine Fallico ◽  
Ferdinando Frega ◽  
Maria Fernanda Rivera Velásquez ◽  
...  
Keyword(s):  
Hydraulic Conductivity ◽  
Spatial Variability ◽  
Hydraulic Properties ◽  
Scaling Laws ◽  
Scaling Analysis ◽  
Field Scale ◽  
Porous Formation ◽  
Proper Design ◽  
First Time

AbstractThe spatial variability of the aquifers' hydraulic properties can be satisfactorily described by means of scaling laws. The latter enable one to relate the small (typically laboratory) scale to the larger (typically formation/regional) ones, therefore leading de facto to an upscaling procedure. In the present study, we are concerned with the spatial variability of the hydraulic conductivity K into a strongly heterogeneous porous formation. A strategy, allowing one to identify correctly the single/multiple scaling of K, is applied for the first time to a large caisson, where the medium was packed. In particular, we show how to identify the various scaling ranges with special emphasis on the determination of the related cut-off limits. Finally, we illustrate how the heterogeneity enhances with the increasing scale of observation, by identifying the proper law accounting for the transition from the laboratory to the field scale. Results of the present study are of paramount utility for the proper design of pumping tests in formations where the degree of spatial variability of the hydraulic conductivity does not allow regarding them as “weakly heterogeneous”, as well as for the study of dispersion mechanisms.

scholarly journals N-Fold Darboux Transformation for the Classical Three-Component Nonlinear Schrödinger Equations and Its Exact Solutions

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 733
Author(s):  
Yu-Shan Bai ◽  
Peng-Xiang Su ◽  
Wen-Xiu Ma
Keyword(s):  
Exact Solutions ◽  
Gauge Transformation ◽  
Darboux Transformation ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Lax Pairs ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
The Given

In this paper, by using the gauge transformation and the Lax pairs, the N-fold Darboux transformation (DT) of the classical three-component nonlinear Schrödinger (NLS) equations is given. In addition, by taking seed solutions and using the DT, exact solutions for the given NLS equations are constructed.

What drives housing prices, rent and new construction in China

2017 ◽  
Vol 10 (5) ◽  
pp. 662-686
Author(s):  
Dimitrios Staikos ◽  
Wenjun Xue
Keyword(s):  
Real Estate ◽  
Empirical Test ◽  
Housing Prices ◽  
Panel Cointegration ◽  
Real Estate Market ◽  
Estimation Methods ◽  
Content Type ◽  
New Construction ◽  
Using Data ◽  
First Time

Purpose With this paper, the authors aim to investigate the drivers behind three of the most important aspects of the Chinese real estate market, housing prices, housing rent and new construction. At the same time, the authors perform a comprehensive empirical test of the popular 4-quadrant model by Wheaton and DiPasquale. Design/methodology/approach In this paper, the authors utilize panel cointegration estimation methods and data from 35 Chinese metropolitan areas. Findings The results indicate that the 4-quadrant model is well suited to explain the determinants of housing prices. However, the same is not true regarding housing rent and new construction suggesting a more complex theoretical framework may be required for a well-rounded explanation of real estate markets. Originality/value It is the first time that panel data are used to estimate rent and new construction for China. Also, it is the first time a comprehensive test of the Wheaton and DiPasquale 4-quadrant model is performed using data from China.

scholarly journals Exact Solutions of the Generalized Nonlinear Schrodinger Equation

2021 ◽  
pp. 18-25
Author(s):  
Gaukhar Shaikhova ◽  
Arailym Syzdykova ◽  
Samgar Daulet
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Physical Problems ◽  
Different Types ◽  
Generalized Nonlinear Schrödinger Equation

In this work, the generalized nonlinear Schrodinger equation is investigated. Exact solutions are derived by the sinecosine method. This method is used to obtain the exact solutions for different types of nonlinear partial differential equations. Graphs of obtained solutions are presented. The obtained solutions are found to be important for the explanation of some practical physical problems.

scholarly journals Some Methods about Finding the Exact Solutions of Nonlinear Modified BBM Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Fan Niu ◽  
Jianming Qi ◽  
Zhiyong Zhou
Keyword(s):  
Exact Solutions ◽  
Rational Function ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Complex Method ◽  
First Time ◽  
Bbm Equation

Finding exact solutions of nonlinear equations plays an important role in nonlinear science, especially in engineering and mathematical physics. In this paper, we employed the complex method to get eight exact solutions of the modified BBM equation for the first time, including two elliptic function solutions, two simply periodic solutions, and four rational function solutions. We used the exp − ϕ z -expansion methods to get fourteen forms of solutions of the modified BBM equation. We also used the sine-cosine method to obtain eight styles’ exact solutions of the modified BBM equation. Only the complex method can obtain elliptic function solutions. We believe that the complex method presented in this paper can be more effectively applied to seek solutions of other nonlinear evolution equations.

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