Search results for "54"
showing 10 items of 2200 documents
Multi-parameters rational solutions to the mKdV equation
2021
N-order solutions to the modified Korteweg-de Vries (mKdV) equation are given in terms of a quotient of two wronskians of order N depending on 2N real parameters. When one of these parameters goes to 0, we succeed to get for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2N real parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 6.
Other patterns for the first and second order rational solutions to the KPI equation
2022
We present rational solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of polynomials in x, y and t depending on several real parameters. We get an infinite hierarchy of rational solutions written as a quotient of a polynomial of degree 2N (N + 1) − 2 in x, y and t by a polynomial of degree 2N (N + 1) in x, y and t, depending on 2N − 2 real parameters for each positive integer N. We construct explicit expressions of the solutions in the simplest cases N = 1 and N = 2 and we study the patterns of their modulus in the (x, y) plane for different values of time t and parameters. In particular, in the study of these solutions, we see the appearance not yet observed of three pairs of…
From particular polynomials to rational solutions to the KPI equation
2022
We construct solutions to the Kadomtsev-Petviashvili equation (KPI) from particular polynomials. We obtain rational solutions written as a second derivative with respect to the variable x of a logarithm of a determinant of order n. So we get with this method an infinite hierarchy of rational solutions to the KPI equation. We give explicitly the expressions of these solutions for the first five orders.
Rational solutions of order N to the KPI equation with multi-parameters and the explicit case of order 3
2022
We present multiparametric rational solutions to the Kadomtsev-Petviashvili equation (KPI). These solutions of order N depend on 2N − 2 real parameters. Explicit expressions of the solutions at order 3 are given. They can be expressed as a quotient of a polynomial of degree 2N (N + 1) − 2 in x, y and t by a polynomial of degree 2N (N + 1) in x, y and t, depending on 2N − 2 real parameters. We study the patterns of their modulus in the (x,y) plane for different values of time t and parameters.
Solutions to the Gardner equation with multiparameters and the rational case
2022
We construct solutions to the Gardner equation in terms of trigonometric and hyperbolic functions, depending on several real parameters. Using a passage to the limit when one of these parameters goes to 0, we get, for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2N parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 3. We easily deduce solutions to the mKdV equation in terms of wronskians as well as rational solutions depending on 2N real parameters.
On the existence of at least a solution for functional integral equations via measure of noncompactness
2017
In this article, we use fixed-point methods and measure of noncompactness theory to focus on the problem of establishing the existence of at least a solution for the following functional integral equation ¶ \[u(t)=g(t,u(t))+\int_{0}^{t}G(t,s,u(s))\,ds,\quad t\in{[0,+\infty[},\] in the space of all bounded and continuous real functions on $\mathbb{R}_{+}$ , under suitable assumptions on $g$ and $G$ . Also, we establish an extension of Darbo’s fixed-point theorem and discuss some consequences.
Wind accretion in the massive X-ray binary 4U 2206+54: abnormally slow wind and a moderately eccentric orbit
2006
Massive X-ray binaries are usually classified depending on the properties of the donor star in classical, supergiant and Be X-ray binaries. The massive X-ray binary 4U 2206+54 does not fit in any of these groups, and deserves a detailed study to understand how the transfer of matter and the accretion on to the compact object take place. To this end we study an IUE spectrum of the donor and obtain a wind terminal velocity (v_inf) of ~350 km/s, which is abnormally slow for its spectral type. We also analyse here more than 9 years of available RXTE/ASM data. We study the long-term X-ray variability of the source and find it to be similar to that observed in the wind-fed supergiant system Vela …
A Universal Length-Dependent Vibrational Mode in Graphene Nanoribbons
2019
Graphene nanoribbons (GNRs) have attracted considerable interest as their atomically tunable structure makes them promising candidates for future electronic devices. However, obtaining detailed information about the length of GNRs has been challenging and typically relies on low-temperature scanning tunneling microscopy. Such methods are ill-suited for practical device application and characterization. In contrast, Raman spectroscopy is a sensitive method for the characterization of GNRs, in particular for investigating their width and structure. Here, we report on a length-dependent, Raman active low-energy vibrational mode that is present in atomically precise, bottom-up synthesized armch…
Convertir de un sistema de coordenadas (CRS) a otro
2009
Convertir de un sistema de coordenadas (CRS) a otro
Creando capa eventos
2008
Creando capa eventos