Two different methods are proposed for the generation of wide classes of exact solutions to the stationary Gross-Pitaevskii equation (GPE). The first method, suggested by the work of Kondrat'ev and Miller [Izv. Vyssh. Uchebn. Zaved., Radiofiz IX, 910 (1966)], applies to one-dimensional (1D) GPE. It is based on the similarity between the GPE and the integrable Gardner equation, all solutions of ...

Homothetic scalar field collapse is considered in this article. By making a suitable choice of variables the equations are reduced to an autonomous system. Then using a combination of numerical and analytic techniques it is shown that there are two classes of solutions. The first consists of solutions with a non-singular origin in which the scalar field collapses and disperses again. There is a...

We provide a detailed investigation of limits of N {soliton solutions of the Toda lattice as N tends to innnity. Our principal results yield new classes of Toda solutions including, in particular, new kinds of soliton{like (i.e., reeectionless) solutions. As a byproduct we solve an inverse spectral problem for one{dimensional Jacobi operators and explicitly construct tri{ diagonal matrices that...

Classification involves associating instances with particular classes by maximizing intra-class similarities and minimizing inter-class similarities. Thus, the way similarity among instances is measured is crucial for the success of the system. In case-based reasoning, it is assumed that similar problems have similar solutions. The case-based approach to classification is founded on retrieving ...