The integrating factor technique is widely used to solve numerically (in particular) the Schrödinger equation in context of spectral methods. Here, we present an improvement this method exploiting freedom provided by gauge condition potential. Optimal conditions are derived considering and temporal numerical resolution with adaptive embedded scheme arbitrary order. We illustrate approach nonlin...

We discuss the phenomenon of preacceleration in the light of a method of successive approximations used to construct the physical order reduction of a large class of singular equations. A simple but illustrative physical example is analyzed to get more insight into the convergence properties of the method. Short title: LETTER TO THE EDITOR

It is well known that provided scalar (1+1)-dimensional evolution equation possesses the infinitedimensional commutative Lie algebra of time-independent non-classical symmetries, it is either linearizable or integrable via inverse scattering transform [1, 2]. The standard way to prove the existence of such algebra is to construct the recursion operator [2]. But Fuchssteiner [3] suggested an alt...