Small data blow-up for a system of nonlinear Schrödinger equations

Abstract We give examples of small data blow-up for a three-component system of quadratic nonlinear Schrodinger equations in one space dimension. Our construction of the blowing-up solution is based on the Hopf–Cole transformation, which allows us to reduce the problem to getting suitable growth estimates for a solution to the transformed system. Amplification in the reduced system is shown to have a close connection with the mass resonance.

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