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Focusing nonlinear Schrodinger equation

{c}

For every $\kappa>0$ and $x_0\in\mathbb R$,
$$
\psi(x,t)=\kappa e^{i\kappa^2t}
\operatorname{sech}(\kappa(x-x_0))
$$
solves $i\psi_t+\psi_{xx}+2|\psi|^2\psi=0$ and decays rapidly as $|x|\to\infty$.


Bright standing soliton of the focusing nonlinear Schrodinger equation

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 1 / 33E / Solution

Bright standing soliton of the focusing nonlinear Schrodinger equation

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Bright standing soliton of the focusing nonlinear Schrodinger equation

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