All Questions
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Intuition behind focusing vs defocusing in integrable systems like NLS, KdV, mKdV
The following are examples of integrable systems arising from the AKNS system (check out AKNS paper here and a short Wikipedia description)
Non-Linear Schrodinger equation
Korteweg-de Vries equation
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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 $\Psi(x,t)$,
$$
i \frac{\partial \Psi}{...
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Nonlinear Saturated Schrodinger Equation in 1D- Physical Models
I'm studying the Nonlinear 1d Schrodinger equation
$$i\psi _t + \psi '' + |\psi |^{2p} \psi - \epsilon |\psi | ^{2q} \psi = 0\, , \quad t>0, x\in \mathbb{R}\, ,$$
and specifically, its solitary ...
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