Search results for " Integra"
showing 10 items of 2527 documents
Degenerate determinant representation of solutions of the NLS equation, higher Peregrine breathers and multi-rogue waves.
2012
We present a new representation of solutions of the focusing NLS equation as a quotient of two determinants. This work is based on a recent paper in which we have constructed a multi-parametric family of this equation in terms of wronskians. This formulation was written in terms of a limit involving a parameter. Here we give a very compact formulation without presence of a limit. This is a completely new result which gives a very efficient procedure to construct families of quasi-rational solutions of the NLS equation. With this method, we construct Peregrine breathers of orders N=4 to 7 and multi-rogue waves associated by deformation of parameters.
Families of quasi-rational solutions of the NLS equation as an extension of higher order Peregrine breathers.
2011
We construct a multi-parametric family of solutions of the focusing NLS equation from the known result describing the multi phase almost-periodic elementary solutions given in terms of Riemann theta functions. We give a new representation of their solutions in terms of Wronskians determinants of order 2N composed of elementary trigonometric functions. When we perform a special passage to the limit when all the periods tend to infinity, we get a family of quasi-rational solutions. This leads to efficient representations for the Peregrine breathers of orders N=1,, 2, 3, first constructed by Akhmediev and his co-workers and also allows to get a simpler derivation of the generic formulas corres…
Quasi-rational solutions of the NLS equation and rogue waves
2010
We degenerate solutions of the NLS equation from the general formulation in terms of theta functions to get quasi-rational solutions of NLS equations. For this we establish a link between Fredholm determinants and Wronskians. We give solutions of the NLS equation as a quotient of two wronskian determinants. In the limit when some parameter goes to $0$, we recover Akhmediev's solutions given recently It gives a new approach to get the well known rogue waves.
Eighth Peregrine breather solution of the NLS equation and multi-rogue waves
2012
This is a continuation of a paper in which we present a new representation of solutions of the focusing NLS equation as a quotient of two determinants. This work was based on a recent paper in which we had constructed a multi-parametric family of this equation in terms of wronskians. \\ Here we give a more compact formulation without limit. With this method, we construct Peregrine breather of order N=8 and multi-rogue waves associated by deformation of parameters.
Deformations of higher order Peregrine breathers and monstrous polynomials.
2013
International audience; In the following, we present two new results about the focusing one dimensional NLS equation : 1. We construct solutions of NLS equation in terms of wronskians. Then performing a special passage to the limit when a parameter tends to 0, we obtain quasi-rational solutions of NLS equation. 2. We construct quasi-rational solutions in terms of determinants without of a limit. Which is new is that we obtain at order N, solutions depending on 2N-2 parameters. 3. When all these parameters are equal to zeros, we recover Peregrine breathers; it is the reason why we call these solutions deformations of Peregrine breathers. \\ Then we deduce new patterns of solutions in the (x,…
Solutions to the NLS equation : differential relations and their different representations
2020
Solutions to the focusing nonlinear Schrödinger equation (NLS) of order N depending on 2N − 2 real parameters in terms of wronskians and Fredholm determinants are given. These solutions give families of quasirational solutions to the NLS equation denoted by vN and have been explicitly constructed until order N = 13. These solutions appear as deformations of the Peregrine breather PN as they can be obtained when all parameters are equal to 0. These quasi rational solutions can be expressed as a quotient of two polynomials of degree N (N + 1) in the variables x and t and the maximum of the modulus of the Peregrine breather of order N is equal to 2N + 1. Here we give some relations between sol…
Determinant representation of NLS equation, Ninth Peregrine breather and multi-rogue waves
2012
This article is a continuation of a recent paper on the solutions of the focusing NLS equation. The representation in terms of a quotient of two determinants gives a very efficient method of determination of famous Peregrine breathers and its deformations. Here we construct Peregrine breathers of order $N=9$ and multi-rogue waves associated by deformation of parameters. The analytical expression corresponding to Peregrine breather is completely given.
Synergistic targeting of FLT3 mutations in AML via combined menin-MLL and FLT3 inhibition
2020
Abstract The interaction of menin (MEN1) and MLL (MLL1, KMT2A) is a dependency and provides a potential opportunity for treatment of NPM1-mutant (NPM1mut) and MLL-rearranged (MLL-r) leukemias. Concomitant activating driver mutations in the gene encoding the tyrosine kinase FLT3 occur in both leukemias and are particularly common in the NPM1mut subtype. In this study, transcriptional profiling after pharmacological inhibition of the menin-MLL complex revealed specific changes in gene expression, with downregulation of the MEIS1 transcription factor and its transcriptional target gene FLT3 being the most pronounced. Combining menin-MLL inhibition with specific small-molecule kinase inhibitors…
Brexit: An Introduction
2020
This section examines the consequences of the United Kingdom (UK)’s decision to leave the EU. Though chapters acknowledge that most will depend on the outcome of the UK–EU negotiations as Brexit will be an unpredictable case of differentiated disintegration. This section offers contributions that aim at stimulating the debate on how Brexit might be understood and analyzed. Will Brexit cause breakdown, heading forward or merely continuous muddling through? The case of Brexit serves as a research laboratory in which we can test existing theories of European integration. Are they able to explain patterns of disintegration equally to integration, or do we need new theoretical and conceptual too…
Biologically based models of cancer risk in radiation research
2020
PURPOSE: In radiation risk analysis the state-of-the-art approach is based on descriptive models which link excess rates of cancer incidence and mortality to radiation exposure by statistical association. To estimate the number of sporadic and radiation-induced cases descriptive models apply parametric dose response function which directly determine the radiation risk. In biologically-based models of cancer risk (BBCR models) dose responses are implemented for key events on the biological level such as early mutations or clonal expansion of initiated cells. Influenced by radiation these events then shape the risk response on the epidemiological level. Although BBCR models facilitate a more …