A slightly modified variant of the cubic periodic one-dimensional nonlinear Schrödinger equation is shown to be well-posed, in a relatively weak sense, in certain function spaces wider than L. Solutions are constructed as sums of infinite series of multilinear operators applied to initial data, and these multilinear operators are analyzed directly.

By using the point canonical transformation approach in a manner distinct from previous ones, we generate some new exactly solvable or quasi-exactly solvable potentials for the one-dimensional Schrödinger equation with a position-dependent effective mass. In the latter case, SUSYQM techniques provide us with some additional new potentials. PACS: 02.30.Gp, 03.65.Ge

A revision of the recursive method proposed by S.A. Shakir [Am. J. Phys. 52, 845 (1984)] to solve bound eigenvalues of the Schrödinger equation is presented. Equations are further simplified and generalized for computing wave functions of any given one-dimensional potential, providing accurate solutions not only for bound states but also for scattering and resonant states, as demonstrated here ...

The one-dimensional oblique propagation of magnetohydrodynamic waves with arbitrary amplitudes in a Hall plasma with isotropic pressure is studied under assumption that the plasma β is large. It is shown that the wave evolution is described by the derivative nonlinear Schrödinger equation (DNLS).

A slightly modified variant of the cubic periodic one-dimensional nonlinear Schrödinger equation is shown to be well-posed, in a relatively weak sense, in certain function spaces wider than L. Solutions are constructed as sums of infinite series of multilinear operators applied to initial data; no fixed point argument or energy inequality are used.

We show that the Nonlinear Schrödinger Equation and the related Lax pair in 1+1 dimensions can be derived from 2+1 dimensional Chern-Simons Topological Gauge Theory. The spectral parameter, a main object for the Loop algebra structure and the Inverse Spectral Transform, has appear as a homogeneous part (condensate) of the statistical gauge field, connected with the compactified extra space coor...

We prove, by adapting the method of Colliander-Kenig [9], local wellposedness of the initial-boundary value problem for the one-dimensional nonlinear Schrödinger equation i∂tu+∂ 2 x u+λu|u|α−1 = 0 on the half-line under low boundary regularity assumptions.

We give a method to solve the time-dependent Schrödinger equation for a system of one-dimensional bosons interacting via a repulsive delta function potential. The method uses the ideas of Bethe Ansatz but does not use the spectral theory of the associated Hamiltonian.

We study the one-dimensional discrete quasi-periodic Schrödinger equation −ϕ(n + 1) − ϕ(n − 1) + λV (x + nω)ϕ(n) = Eϕ(n), n ∈ Z We show that for " typical " C 3 potential V , if the coupling constant λ is large, then for most frequencies ω, the Lyapunov exponent is positive for all energies E, and the corresponding eigenfunctions ϕ decay exponentially.

We establish quantitative bounds on the rate of approach to equilibrium for a system with infinitely many degrees of freedom evolving according to a one-dimensional focusing nonlinear Schrödinger equation with diffusive forcing. Equilibrium is described by a generalized grand canonical ensemble. Our analysis also applies to the easier case of defocusing nonlinearities. .