# Solving Higher-Order Kinetic Energy Term (Gross-Pitaevskii equation) [closed]

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).

• Not sure what exactly you are asking for here. – flippiefanus Sep 25 '16 at 11:00
• @flippiefanus, to solve with second order derivatives. – user0322 Sep 25 '16 at 11:20
• @flippiefanus, my questions is to solve a modified equation with a higher-order kinetic energy term. – user0322 Sep 25 '16 at 11:26
• @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? – anon01 Sep 25 '16 at 12:02
• @ConfusinglyCuriousTheThird, just to make it clear to flippiefanus – user0322 Sep 25 '16 at 12:15