[PDF] Top 20 Solutions of the Schrödinger equation in a Hilbert space

... the equation does not have an ...the Schrödinger equation, we develop the technique of generalized inverse operators [–] for the original linear operator in Banach and Hilbert ... See full document

... radial solutions to a cubic NLS equation in dimension ...nonlinear Schrödinger–Korteweg–de Vries ...linear Schrödinger equation with a point singular ...linear Schrödinger ... See full document

... nonlinear Schrödinger equation with an x-periodic and t-quasi-periodic quintic nonlinear ...the equation admits small-amplitude, linearly stable, real analytic, and quasi-periodic solutions ... See full document

... dimensional Schrödinger equation with a cubic nonlinearity has been known for a long time as well as its analytical solutions in terms of sech-shaped ...dimensional Schrödinger equation ... See full document

... state solutions of the Schrödinger equation with generalized inverted hyperbolic potential using the Niki- forov-Uvarov method are ...energy equation and the wave function for these spe- cial ... See full document

... fractional Schrödinger equation, in which the normal Schrödinger equation is generalized in anal- ogy with fractional ...this equation in the case of the one-dimensional infinite square ... See full document

... nonlinear Schrödinger equations are used in the fiber optics, nonlinear photonics and optical wave turbulence, see for instance a recent review paper [51] by Turitsyn et ...nonlinear Schrödinger equations ... See full document

... the Schrödinger equation is solved by Modified separation of variables (MSV) method suggested by Pishkoo and ...G-function solutions are derived in cylindrical coordinate system for quantum particle ... See full document

... for solutions of the stationary Schrödinger equation on ...for solutions of the Dirichlet problem with respect to the Schrödinger operator on cones and the growth property of ... See full document

... approximate solutions of the variable-coefficient fractional Schrödinger equation (VFNLS) with time and space fractional ...analytical solutions and their structure of the VFNLS are ... See full document

... fractional Schrödinger equation (– ) α u + V(x)u = f (x,u), x ∈ R N , where 0 < α < 1, N > 2 α , (– ) α stands for the fractional Laplacian of order α , V is a positive continuous potential, and f ... See full document

... In this paper, we consider a fractional Schrödinger equation with steep potential well and sublinear perturbation. By virtue of variational methods, the existence criteria of infinitely many nontrivial high ... See full document

... mixed solutions of the DNLS equation and their degeneration mechanism, which implies the obtaining of rogue waves by the synchronization of the mixed solutions: phase solutions and breather ... See full document

... Under the conditions of Proposition 2.1 or Theorem 2.3 which are NOT covered by Proposition 2.5, we have not been able to construct a Lyapunov function using the method in [5], mainly because of our system’s singular ... See full document

... of solutions of the NLS equation are considered to be prototypes of rogue ...(SPB) solutions (see Figs. 1 and 2). Time-periodic breather-type solutions as well as rational solutions, ... See full document

... [10] Vergara, V. and Zacher, R. (2017) Stability, Instability, and Blowup for Time Frac- tional and Other Nonlocal in Time Semilinear Subdiffusion Equations. Journal of Evolution Equations , 17, 599-626. ... See full document

... considered ground state solutions of the corresponding quasilinear Schrödinger systems for (.) by the same methods and obtained similar results. For the stability and instabil- ity results for the special ... See full document

... The method of the proof of the theorems concerning the quasiuniqueness of the solution of 0.1-0.2 presented in sctions 2 an 3 allows one to assert, even in cases when there is no quasiun[r] ... See full document

... In order to prove the nonexistence of solution to (1.8), we use the test function method, which has been used in [5, 9] to deal with the m-Laplace equation. The proof is by con- tradiction which involves obtaining ... See full document

... the solutions of ordinary second-order linear homogeneous differential ...radial Schrödinger equation when a Coulomb potential is used to describe the hydrogen ... See full document