9 citations · 25 across the 7 of their papers we have counts for
7 papers
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…
Monotonicity of the first Dirichlet eigenvalue of regular polygons
Joel Dahne, Javier Gómez-Serrano, Joana Pech-Alberich
In this paper we prove that the first Dirichlet eigenvalue of an -sided regular polygon of fixed area is a monotonically decreasing function of for all , a…
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…
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…
Highest Cusped Waves for the Burgers-Hilbert equation
Joel Dahne, Javier Gómez-Serrano
In this paper we prove the existence of a periodic highest, cusped, traveling wave solution for the Burgers-Hilbert equation and give its asymptotic behavi…
A counterexample to Payne's nodal line conjecture with few holes
Joel Dahne, Javier Gómez-Serrano, Kimberly Hou
Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the boundary of the domain. In their 1997 breakthrough paper, Hoffmann-Ostenhof, Hoff…
Computation of Tight Enclosures for Laplacian Eigenvalues
Joel Dahne, Bruno Salvy
Recently, there has been interest in high-precision approximations of the first eigenvalue of the Laplace-Beltrami operator on spherical triangles for combinatorial purposes. We co…