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Classification of traveling waves for a quadratic Szegő equation

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  • We give a complete classification of the traveling waves of the following quadratic Szegő equation :

    $i{\partial _t}u = 2J\Pi \left( {{{\left| u \right|}^2}} \right) + \bar J{u^2},\;\;\;\;u\left( {0, \cdot } \right) = {u_0},$

    and we show that they are given by two families of rational functions, one of which is generated by a stable ground state. We prove that the other branch is orbitally unstable.

    Mathematics Subject Classification: 37K10, 35C07, 37K45.

    Citation:

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  • Figure 1.  The action of $ H_u $, $ K_u $ and $ S^* $ on $ F $

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