Rational solitons of wave resonant-interaction models

Integrable models of resonant interaction of two or more waves in 1+1 dimensions are known to be of applicative interest in several areas. Here we consider a system of three coupled wave equations which includes as special cases the vector nonlinear Schrödinger equations and the equations describing the resonant interaction of three waves. The Darboux-Dressing construction of soliton solutions is applied under the condition that the solutions have rational, or mixed rational-exponential, dependence on coordinates. Our algebraic construction relies on the use of nilpotent matrices and their Jordan form. We systematically search for all bounded rational (mixed rational-exponential) solutions and find a broad family of such solutions of the three wave resonant interaction equations

Cyst nematodes of the genus Heterodera and Globodera in Sicily

A survey was conducted in Sicily, from 2007 to 2009, to obtain insights on specific composition, frequency and geographical distribution of cyst nematodes associated to crops of agricultural economic importance. Soil and root samples were collected mainly from crops showing chlorosis, poor growth and reduced yield. Cysts and larvae were extracted and identified to species level by comparative examination of morphological and morphometric characters. Confirmation of the species identity was also made by molecular analysis for some species. Seven species of the genus Heterodera Schmidt, 1871 and two of the genus Globodera Skarbilovic, 1959 were found. They were H. avenae Wollenweber, 1924, H. bifenestra Cooper, 1955, H. carotae Jones, 1950, H. goettingiana Liebscher, 1892, H. hordecalis Andersson, 1974, H. latipons Franklin, 1969 and H. schachtii Schmidt, G. rostochiensis (Wollenweber, 1923) Behrens, 1975 and G. pallida (Stone, 1973) Behrens, 1975. All species dectected are known to occur in Europe and the Mediterranean basin, but H. avenae, H. hordecalis, and H. latipons had not been reported from Sicily and H. bifenestra is a new report for Italy