scholarly journals Two new Painlevé integrable KdV–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation and new negative-order KdV-CBS equation

Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Author(s):  
V. V. Makarov ◽  
D. A. Lozovoy

  Enzootic bovine leucosis (EBL) has been known for more than a century and a half. Its occurrence and registration may have historically been associated with intensive breeding of dairy cattle in Western Europe to increase target productivity. It is known that any limiting intervention in the nature of the animal organism is always accompanied by an uncontrolled and unpredictable change in the genotype of a wider range than the required, particularly negative order. In particular, a decrease in the resistance to macroorganisms and the possibility of the new diseases emergence, including infectious ones (for example, immunodeficiencies such as BLAD syndrome of black-motley cattle and stress syndrome in pigs, the occurrence of scrapie and other slow sheep infections). In the last two decades of the last century, in many disadvantaged countries, primarily Western European, national programs for the eradication of EBL have been developed and subsequently successfully implemented. First of all the motivation was the economy of dairy cattle breeding (mainly the extension of productive age, as well as the tightening of requirements in international trade in cattle and bull products, breeding, pricing, etc.). In an analytical article are reviewed the elements of epizootology of EBL in the foreign countries with special attention to the situation in the USA, scenarios of various control programs, and promising methods for assessing the role of infected animals in the epizootic process. A critical assessment of the problem of EBL in the Russian Federation is given, the reasons for the ineffectiveness of against leucosis measures are discussed.


Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 224
Author(s):  
Ghaylen Laouini ◽  
Amr M. Amin ◽  
Mohamed Moustafa

A comprehensive study of the negative-order Kadomtsev–Petviashvili (nKP) partial differential equation by Lie group method has been presented. Initially the infinitesimal generators and symmetry reduction, which were obtained by applying the Lie group method on the negative-order Kadomtsev–Petviashvili equation, have been used for constructing the reduced equations. In particular, the traveling wave solutions for the negative-order KP equation have been derived from the reduced equations as an invariant solution. Finally, the extended improved (G′/G) method and the extended tanh method are described and applied in constructing new explicit expressions for the traveling wave solutions. Many new and more general exact solutions are obtained.


Author(s):  
J.-G. Bak ◽  
D. McMichael ◽  
D. Oberlin

AbstractTheorems 1 and 2 are known results concerning Lp–Lq estimates for certain operators wherein the point (1/p, 1/q) lies on the line of duality 1/p + 1/q = 1. In Theorems 1′ and 2′ we show that with mild additional hypotheses it is possible to prove Lp-Lq estimates for indices (1/p, 1/q) off the line of duality. Applications to Bochner-Riesz means of negative order and uniform Sobolev inequalities are given.


2018 ◽  
Vol 33 (35) ◽  
pp. 1850209 ◽  
Author(s):  
H. Wajahat A. Riaz ◽  
Mahmood ul Hassan

A noncommutative negative order AKNS (NC-AKNS(-1)) equation is studied. To show the integrability of the system, we present explicitly the underlying integrable structure such as Lax pair, zero-curvature condition, an infinite sequence of conserved densities, Darboux transformation (DT) and quasideterminant soliton solutions. Moreover, the NC-AKNS(-1) equation is compared with its commutative counterpart not only on the level of nonlinear evolution equation but also for the explicit solutions.


2021 ◽  
Author(s):  
Andriy E. Serebryannikov ◽  
Diana C. Skigin ◽  
Guy A. E. Vandenbosch ◽  
Ekmel Ozbay

Abstract The concept of multifunctional reflection-mode gratings based on rod-type photonic crystals with C2 symmetry is introduced and examined. The specific modal properties lead to the vanishing dependence of the first-negative-order maximum on the angle of incidence within a wide range, and the nearly sinusoidal redistribution of the incident-wave energy between zero order (specular reflection) and first negative diffraction order (deflection) at frequency variation that are the key features enabling various functionalities in one structure and functionality merging. The elementary functionalities offered by the studied structures, of which multifunctional scenarios can be designed, include but are not restricted to multiband spatial filtering, multiband splitting, and demultiplexing. The proposed structures are shown to be capable in multifunctional operation in case of an obliquely incident polychromatic wave. The generalized demultiplexing is demonstrated for the case when several polychromatic wavesare incident at different angles. The same deflection properties yield multiband splitting, and merging demultiplexing and splitting functionalties in one functionality, which may contribute to various multifunctional scenarios. The proposed gratings arealso studied in transmissive configuration.


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