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Junior Research Group Nonlinear Helmholtz Equations

Junior Research Group "Nonlinear Helmholtz Equations"

This is the webpage of the Junior Research Group "Nonlinear Helmholtz equations", existent since July 1st 2016 as an associated project (AP2) with the Collaborative Research Center 1173. Please have a look at these pages for more detailed information.


Staff in the Junior Research Group Nonlinear Helmholtz Equations
Name Tel. E-Mail
PD Dr. Rainer Mandel +49 721 608 46178 rainer.mandel@kit.edu
Dr. Dominic Scheider 0049 721 608 42046 dominic.scheider@kit.edu

Current Offering of Courses
Semester Titel Typ
Summer Semester 2020 Nichtlineare Funktionalanalysis Lecture
Summer Semester 2018 Boundary and Eigenvalue Problems Lecture
Winter Semester 2017/18 Variational and Topological Methods in Bifurcation Theory Lecture
Seminar Bifurcation Theory Seminar
Summer Semester 2017 Bifurcation Theory Lecture

Guests in our group


Publications of the Junior Research Group since July 1st 2016


  1. link R.Mandel, E.Montefusco, B.Pellacci: Oscillating solutions for nonlinear Helmholtz equations. Z. Angew. Math. Phys. 68 (2017), no. 6, Art. 121, 19 pp.
  2. link R.Mandel, D.Scheider: Dual variational methods for a nonlinear Helmholtz system. NoDEA Nonlinear Differential Equations Appl. 25 (2018), no. 2, 25:13.
  3. link R.Mandel: The limiting absorption principle for periodic differential operators and applications to nonlinear Helmholtz equations, Commun. Math. Phys. 368 (2019), no. 2 799-842.
  4. link D.Bonheure, J.-B.Casteras, R.Mandel: On a fourth order nonlinear Helmholtz equation, Journal of the London Mathematical Society 99 (2019), no. 3, 831-852.
  5. link R.Mandel, D.Scheider: Bifurcations of nontrivial solutions of a cubic Helmholtz system, Advances in Nonlinear Analysis, 9(1), 1026–1045.
  6. link R.Mandel: Uncountably many solutions for nonlinear Helmholtz and curl-curl equations with general nonlinearities, Adv. Nonlinear Stud. 19 (2019), no. 3, 569-593.
  7. link J.-B.Casteras, R.Mandel: On Helmholtz equations and counterexamples to Strichartz estimates in hyperbolic space.
  8. link R.Mandel: Dispersive estimates, blow-up and failure of Strichartz estimates for the Schrödinger equation with slowly decaying initial data,

Pure And Applied Analysis, vol. 2 (2020), No. 2, 519-532.

  1. link (Preprint) R.Mandel, D.Scheider: An annulus multiplier and applications to the Limiting absorption principle for Helmholtz equations with a step potential.
  2. link (Preprint) R.Mandel, D.Scheider: Variational methods for breather solutions of Nonlinear Wave Equations.
  3. link (Preprint) L.Cossetti, R.Mandel: A limiting absorption principle for Helmholtz systems and time-harmonic isotropic Maxwell's equations.



Publications in Projekt B3 of our CRC1173 since 01.07.2016

  1. link R.Mandel, W.Reichel: A priori bounds and global bifurcations results for frequency combs modeled by the Lugiato-Lefever equation. SIAM J. Appl. Math. 77 (2017), no. 1, 315–345.
  2. link R.Mandel: Global secondary bifurcation, symmetry breaking and period-doubling.
  3. link J. Gärtner, P. Trocha, R. Mandel, C. Koos, T. Jahnke, W. Reichel: Bandwidth and conversion efficiency analysis of dissipative Kerr soliton frequency combs based on bifurcation theory, Phys. Rev. A 100, 033819
  4. link (Preprint) J.Gärtner, R.Mandel, W.Reichel: The Lugiato-Lefever equation with nonlinear damping caused by two photon absorption.

Further research activities