189 research outputs found
Acoustic Scattering and the Extended Korteweg deVries hierarchy
The acoustic scattering operator on the real line is mapped to a
Schr\"odinger operator under the Liouville transformation. The potentials in
the image are characterized precisely in terms of their scattering data, and
the inverse transformation is obtained as a simple, linear quadrature. An
existence theorem for the associated Harry Dym flows is proved, using the
scattering method. The scattering problem associated with the Camassa-Holm
flows on the real line is solved explicitly for a special case, which is used
to reduce a general class of such problems to scattering problems on finite
intervals.Comment: 18 page
On Soliton Content of Self Dual Yang-Mills Equations
Exploiting the formulation of the Self Dual Yang-Mills equations as a
Riemann-Hilbert factorization problem, we present a theory of pulling back
soliton hierarchies to the Self Dual Yang-Mills equations. We show that for
each map \C^4 \to \C^{\infty } satisfying a simple system of linear
equations formulated below one can pull back the (generalized) Drinfeld-Sokolov
hierarchies to the Self Dual Yang-Mills equations. This indicates that there is
a class of solutions to the Self Dual Yang-Mills equations which can be
constructed using the soliton techniques like the function method. In
particular this class contains the solutions obtained via the symmetry
reductions of the Self Dual Yang-Mills equations. It also contains genuine 4
dimensional solutions . The method can be used to study the symmetry reductions
and as an example of that we get an equation exibiting breaking solitons,
formulated by O. Bogoyavlenskii, as one of the dimensional reductions
of the Self Dual Yang-Mills equations.Comment: 11 pages, plain Te
Multipeakons and a theorem of Stieltjes
A closed form of the multi-peakon solutions of the Camassa-Holm equation is
found using a theorem of Stieltjes on continued fractions. An explicit formula
is obtained for the scattering shifts.Comment: 6 page
Mixed type Hermite-Padé approximation inspired by the Degasperis-Procesi equation
In this work we present new results on the convergence of diagonal sequences of certain mixed type Hermite-PadĂ© approximants of a Nikishin system. The study is motivated by a mixed Hermite-PadĂ© approximation scheme used in the construction of solutions of a Degasperis-Procesi peakon problem and germane to the analysis of the inverse spectral problem for the discrete cubic string.This author [G.L.L] was supported by research grant MTM2015-65888-C4-2-P of Ministerio de EconomĂa, Industria y Competitividad. This author [S.M.P.] received support from research grant CONICYT Fondecyt/Postdoctorado/ Proyecto 3170112. [J.S] Partially supported by NSERC
Assessment of Wild Mustard (Sinapis arvensis L.) Resistance to ALS-inhibiting Herbicides
There is an urgent need for rapid, accurate, and economical screening tests that can determine if weeds surviving a herbicide application are resistant. This chapter describes development and application of a simple root length bioassay technique for detection of wild mustard (Sinapis arvensis L.) resistance to ALS-inhibiting herbicides. This bioassay was performed in 2-oz WhirlPak® bags filled with 50 g of soil wetted to 100% moisture content at field capacity. Wild mustard seeds were pre-germinated in darkness in Petri dishes lined with moist filter paper for 2 days. Six seeds with well-developed radicles were planted in the non-treated soil and in soil with added herbicide, and plants were grown in a laboratory under fluorescent lights. After 4 days of growth, WhirlPak® bags were cut open, soil was washed away, intact plants were removed, and root length was measured with a ruler. The concentration of each herbicide in soil at which a significant root inhibition of susceptible biotype, but no root inhibition of a resistant biotype occurred was selected. Susceptibility/resistance of wild mustard populations was estimated by calculating the percentage of uninhibited roots of plants grown in the herbicide-treated soil as compared to the plants grown in the non-treated soil
Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two--matrix model
We apply the nonlinear steepest descent method to a class of 3x3
Riemann-Hilbert problems introduced in connection with the Cauchy two-matrix
random model. The general case of two equilibrium measures supported on an
arbitrary number of intervals is considered. In this case, we solve the
Riemann-Hilbert problem for the outer parametrix in terms of sections of a
spinorial line bundle on a three-sheeted Riemann surface of arbitrary genus and
establish strong asymptotic results for the Cauchy biorthogonal polynomials.Comment: 31 pages, 12 figures. V2; typos corrected, added reference
Moment determinants as isomonodromic tau functions
We consider a wide class of determinants whose entries are moments of the
so-called semiclassical functionals and we show that they are tau functions for
an appropriate isomonodromic family which depends on the parameters of the
symbols for the functionals. This shows that the vanishing of the tau-function
for those systems is the obstruction to the solvability of a Riemann-Hilbert
problem associated to certain classes of (multiple) orthogonal polynomials. The
determinants include Haenkel, Toeplitz and shifted-Toeplitz determinants as
well as determinants of bimoment functionals and the determinants arising in
the study of multiple orthogonality. Some of these determinants appear also as
partition functions of random matrix models, including an instance of a
two-matrix model.Comment: 24 page
Effect of soil pH on sulfentrazone phytotoxicity
Non-Peer Reviewe
- …