We analyze the behavior of positive solutions of elliptic equations with a degenerate logistic nonlinearity and Dirichlet boundary conditions. Our results concern existence and strong localization in the spatial region in which the logistic nonlinearity cancels. This type of nonlinearity has applications in the nonlinear Schrodinger equation and the study of Bose-Einstein condensates. In this c...

We study the bound states of a Kronig Penney potential for a nonlinear one-dimensional Schrodinger equation. This potential consists of a large, but not necessarily infinite, number of equidistant δ-function wells. We show that the ground state can be highly degenerate. Under certain conditions furthermore, even the bound state that would be normally the highest can have almost the same energy ...

In this paper we utilize the covariance of Riccati equation with respect to linear fractional transformations to define classes of conformally equivalent second order differential equations. This motivates then the introduction of fractional Darboux transformations which can be recognized also as generalized Cole-Hopf transformations. We apply these transformations to find Schrodinger equations...

We study formation and interaction of one-dimensional screening solitons in a photorefractive medium with sublinear dependence of the photoconductivity on light intensity. We find an exact analytical solution to the corresponding nonlinear Schrodinger equation. We show that these solitons are stable in propagation and their interaction is generic for solitons of saturable nonlinearity. In parti...

Gauge equivalence between the two-dimensional continuous classical Heisenberg ferromagnets(CCHF) of spin 1 2 -the M-I equation with singleside anisotropy and the Zakharov equation(ZE) is established for the easy axis case. The anisotropic CCHF is shown to be gauge equivalent to the isotropic CCHF. Preprint CNLP-1994-05. Alma-Ata.1994 In the study of 1+1 dimensional ferromagnets, a well known La...

We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction defined by a term proportional to 1/jn mj. Continuous medium equation for this system can be obtained in the socalled infrared limit when the wave number tends to zero. We construct a transform operator that maps the system of large number of ordinary differential equations of mot...

Statistical mechanics of the discrete nonlinear Schrodinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of T = infinity, we identify a phase transition through a discontinuity in the partition function. The phase transition is ...

We study the generalized third-order nonlinear Schrodinger (NLS) equation which admits a one-parameter family of single-hump embedded solitons. Analyzing the spectrum of the linearization operator near the embedded soliton, we show that there exists a resonance pole in the left half-plane of the spectral parameter, which explains linear stability, rather than nonlinear semistability, of embedde...