Try to solve the time-independent version of the non-linear Schrödinger equation (TI-NLSE) by iteration. After each iteration step, take the resulting wave function and construct the "potential" for the next iteration step.
To get started, we could begin with the cubic and the logarithmic TI-NLSE, see corresponding Wikipedia articles.
Later perhaps also the TD-NLSE which supports 'breathers', see corresponding Wikipedia articles.
Should discuss this also with Dr. Shalva Amiranashvili @ WIAS
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To get started, we could begin with the cubic and the logarithmic TI-NLSE, see corresponding Wikipedia articles.
Later perhaps also the TD-NLSE which supports 'breathers', see corresponding Wikipedia articles.
Should discuss this also with Dr. Shalva Amiranashvili @ WIAS