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Consider now propagation of non-linear waves in one-dimensional chain of dimers governed by the non-linear Schrödinger equation for the normalized wave envelope $\Psi(x,t)$, $$ i \frac{\partial \Psi}{\partial t}+\frac {1} {2}\frac{\partial^2\Psi}{\partial x^2}+\alpha\vert{\Psi}\vert^2\Psi=0, \tag 1 $$ where $t$ is time or propagation variable, $x$ is the spatial coordinate, and $\alpha$ describes the non-linearity or interaction strength. I would like to solve numerically the Gross-Pitaevski Eq. (1).

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    $\begingroup$ Not sure what exactly you are asking for here. $\endgroup$ – flippiefanus Sep 25 '16 at 11:00
  • $\begingroup$ @flippiefanus, to solve with second order derivatives. $\endgroup$ – user0322 Sep 25 '16 at 11:20
  • $\begingroup$ @flippiefanus, my questions is to solve a modified equation with a higher-order kinetic energy term. $\endgroup$ – user0322 Sep 25 '16 at 11:26
  • $\begingroup$ @DavidH you say an awful lot before you ever get to a question (actually you never ask one!). why don't you make it more concise? $\endgroup$ – anon01 Sep 25 '16 at 12:02
  • $\begingroup$ @ConfusinglyCuriousTheThird, just to make it clear to flippiefanus $\endgroup$ – user0322 Sep 25 '16 at 12:15