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math.AP2026
Non-uniqueness for the Complex Ginzburg-Landau Equation
Joel Dahne, Vladimír Šverák
We show that singularities of the three-dimensional cubic complex Ginzburg-Landau equation developing from smooth initial data can induce non-uniqueness of solutions after the time…
math.AP2024
Self-Similar Singular Solutions to the Nonlinear Schrödinger and the Complex Ginzburg-Landau Equations
Joel Dahne, Jordi-Lluís Figueras
We prove the existence of radial self-similar singular solutions for the mass supercritical Nonlinear Schrödinger Equation far from the critical regime and, more generally, branche…
math.AP2023
Highest Cusped Waves for the Fractional KdV Equations
Joel Dahne
In this paper we prove the existence of highest, cusped, traveling wave solutions for the fractional KdV equations for all and give their ex…