Lie symmetry analysis is an established method for generating symmetries of differential equations. We apply this together the generalized fundamental theorem double reduction. In particular, Noether and some associated conservation laws are constructed in our investigation to find exact solutions higher order partial equations complex

in this paper, the numerical solution methods of one- particale, one – dimensional time- independentschrodinger equation are presented that allows one to obtain accurate bound state eigen values andeigen functions for an arbitrary potential energy function v(x). these methods included the fem(finite element method), cooly, numerov and others. here we considered the numerov method inmore details...

We prove the scattering for a defocusing nonlinear Schrodinger equation with sum of two repulsive potentials strictly convex level surfaces, thus providing result in trapped setting similar to exterior obstacles.

We investigate the approximate l-state solutions of Schrödinger equation for Hulthén plus a class Yukawa potential. In this context, we construct bound-state energy and wavefunction expressed by Gauss hypergeometric function means asymptotic iteration approach in detail.

The solution of one-dimensional Schrodinger equation for a newly proposed potential called modified shifted Deng-Fan momentum-dependent is obtained via supersymmetric approach. expectation values momentum and position were calculated using Hellmann Feynman Theorem. effects parameter on the solutions system as well studied. Finally, special cases interacting obtained.

We consider the Schrödinger equation on a compact manifold, in the presence of a nonlinear damping term, which is homogeneous and sublinear. For initial data in the energy space, we construct a weak solution, defined for all positive time, which is shown to be unique. In the one-dimensional case, we show that it becomes zero in finite time. In the two and three-dimensional cases, we prove the s...