Related papers: On some nonlinear Schr\"odinger equations in $\bbr…
In this paper, we prove new Strichartz estimates for linear Schrodinger equations posed on d-dimensional irrational tori. Then, we use these estimates to prove subcritical and critical local well-posedness results for nonlinear Schrodinger…
Various origins of linear and nonlinear Schrodinger equations are discussed in connection with diffusion, hydrodynamics, and fractal structure. The treatment is mainly expository, emphasizing the quantum potential, with a few new…
We study the periodic non-linear Schrodinger equations with odd integer power nonlinearities, for initial data which are assumed to be small in some negative order Sobolev space, but which may have large L^2 mass. These equations are known…
We prove some multiplicity results for a nonlinear equation of Schroedinger type with potential functions
In this paper we investigate the existence of positive solutions and ground state solution for a class of fractional Schr\"odinger-Poisson equations in $\mathbb R^3$ with general nonlinearities.
We consider the existence and multiplicity of solutions for a class of quasi-linear Schr\"{o}dinger equations which include the modified nonlinear Schr\"{o}dinger equations. A new perturbation approach is used to treat the sub-cubic…
The recently introduced scheme [20,21] is extended to propose an algebraic non-perturbative approach for the analytical treatment of Schr\"odinger equations with non-solvable potentials involving an exactly solvable potential form together…
We develop a high accuracy power series method for solving partial differential equations with emphasis on the nonlinear Schr\"odinger equations. The accuracy and computing speed can be systematically and arbitrarily increased to orders of…
By using AKNS scheme and soliton connection taking values in N=1 superconformal algebra we obtain new coupled super Nonlinear Schrodinger equations.
We consider the stochastic nonlinear Schr\"odinger equations (SNLS) posed on $d$-dimensional tori with either additive or multiplicative stochastic forcing. In particular, for the one-dimensional cubic SNLS, we prove global well-posedness…
We study a 1D nonlinear Schr{\"o}dinger equation appearing in the description of a particle inside an atomic nucleus. For various nonlinearities, the ground states are discussed and given in explicit form. Their stability is studied…
General features of nonlinear quantum mechanics are discussed in the context of applications to two-level atoms.
We analyze initial-boundary value problems for an integrable generalization of the nonlinear Schr\"odinger equation formulated on the half-line. In particular, we investigate the so-called linearizable boundary conditions, which in this…
From non-linear theory of electromagnetism, suggested in (physics/9801031), follows that non-relativistic equation for scalar potential of electron in the field of nuclei is equivalent to respective Schr\"odinger equation. For mass and…
Some focusing coupled Schrodinger equations are investigated. First, existence of ground state is obtained. Second, global and non global existence of solutions are discussed via potential-well method. Finally, strong instability of…
In this work we shall review some of our recent results concerning unique continuation properties of solutions of Schr\"odinger equations. In this equations we include linear ones with a time depending potential and semi-linear ones.
A class of generalized Schr\"{o}dinger elliptic problems involving concave-convex and other types of nonlinearities is studied. A reasonable overview about the set of solutions is provided when the parameters involved in the equation assume…
In this work we study the initial boundary value problem associated with the coupled Schr\"odinger equations {with quadratic nonlinearities, that appears in nonlinear optics}, on the half-line. We obtain local well-posedness for data {in…
We obtain new coupled super Nonlinear Schrodinger equations by using AKNS scheme and soliton connection taking values in N=2 superconformal algebra.
The paper studies existence of solutions for the nonlinear Schr\"odinger equation with a general bounded external magnetic field. In particular, no lattice periodicity of the magnetic field or presence of external electric field is…