Searching for integrable systems and constructing their exact solutions are of both theoretical and practical value. In this paper, Ablowitz–Kaup–Newell–Segur spectral problem and its time evolution equation are first generalized by embedding a new spectral parameter. Based on the generalized AKNS spectral problem and its time evolution equation, Lax integrability of a nonisospectral integrodifferential system is then verified. Furthermore, exact solutions of the nonisospectral integrodifferential system are formulated through the inverse scattering transform method. Finally, in the case of reflectionless (...) potentials, the obtained exact solutions are reduced ton-soliton solutions. Whenn=1andn=2, the characteristics of soliton dynamics of one-soliton solutions and two-soliton solutions are analyzed with the help of figures. (shrink)

From the end of the First World War, a broad discussion took place within the framework of the revived German constitutional teaching on the question of the physical normality of man. The founder of the so-called statistical concept of normality, which preceded the still widespread normal (reference) interval concept, is H. Rautmann, who gave it the character of a tool for discriminating between health and disease. Among some of his successors (Bauer, Borchardt, Günther), however, it was considered more a means (...) of establishing a type, without supposing any precise relation between the frequency of a character in the population and the probability of the occurrence of disease. The concept of a statistical norm as a certain region of the variation range of a character determined by the parameters of Gaussian distribution was criticized both by the supporters of the ideal norm (Hildebrandt) and those who were in favour of a ‘personal’ norm (Grote). The underlying motifs of these three conceptions of normality influenced German constitutional doctrine until after the end of the Second World War, but without a satisfactory solution to the diagnosis of physical normality being found. Since the 1950s, world medicine has moved more and more in the direction of prevention, with the emphasis on a study of individual dispositions to disease and its precursors. In this connection a new view of health has gained importance whereby it is considered a smoothly gradated condition, not sharply distinguished from disease (‘continual’ model of health and disease as opposed to the previous ‘alternative’ model). The purpose of diagnostic characters is no longer merely to place patients in clearly defined categories as healthy or affected by one disease or another, but has taken on the function of indices of the disposition to disease among those who exhibit ‘gross normality’. Discrimination between the alternative and continuous models allows a clarification to be made of the sources of the confusion in which the pre-war concept of statistical normality had found itself. Today many exceptions are known to the rule that the functional optimum lies in the region of the population mean, both for the population as a whole and for individuals; and immense variability has been found in the manner in which individuals in the population attain health. Thus a distinction between health and disease by statistical means alone (such as establishing some sort of species design) is not possible at all. The ideal of a personal norm is pursued today through the concept of a multivariate norm backed up by modern data processing methods, though it was anticipated in principle by Kaup even in the 1920s. CiteULike Connotea Del.icio.us What's this? (shrink)