Pattern Formation and Solitons

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New submissions for Fri, 10 May 24

[1]  arXiv:2405.05441 [pdf, other]

Title: Insensitive edge solitons in non-Hermitian topological lattices

Authors: Bertin Many Manda, Vassos Achilleos

Comments: 5 figures

Subjects: Pattern Formation and Solitons (nlin.PS)

In this work, we demonstrate that the synergetic interplay of topology, nonreciprocity and nonlinearity is capable of unprecedented effects. We focus on a nonreciprocal variant of the Su-Shrieffer-Heeger chain with local Kerr nonlinearity. We find a continuous family of non-reciprocal edge solitons (NESs) emerging from the topological edge mode, with near-zero energy, in great contrast from their reciprocal counterparts. Analytical results show that this energy decays exponentially towards zero when increasing the lattice size. Consequently, despite the absence of chiral symmetry within the system, we obtain zero-energy NESs, which are insensitive to growing Kerr nonlinearity. Even more surprising, these zero-energy NESs also persist in the strong nonlinear limit. Our work may enable new avenues for the control of nonlinear topological waves without requiring the addition of complex chiral-preserving nonlinearities.

Cross-lists for Fri, 10 May 24

[2]  arXiv:2405.05897 (cross-list from math.NA) [pdf, other]

Title: Efficient numerical computation of spiral spectra with exponentially-weighted preconditioners

Authors: Stephanie Dodson, Ryan Goh, Bjorn Sandstede

Subjects: Numerical Analysis (math.NA); Dynamical Systems (math.DS); Pattern Formation and Solitons (nlin.PS)

The stability of nonlinear waves on spatially extended domains is commonly probed by computing the spectrum of the linearization of the underlying PDE about the wave profile. It is known that convective transport, whether driven by the nonlinear pattern itself or an underlying fluid flow, can cause exponential growth of the resolvent of the linearization as a function of the domain length. In particular, sparse eigenvalue algorithms may result in inaccurate and spurious spectra in the convective regime. In this work, we focus on spiral waves, which arise in many natural processes and which exhibit convective transport. We prove that exponential weights can serve as effective, inexpensive preconditioners that result in resolvents that are uniformly bounded in the domain size and that stabilize numerical spectral computations. We also show that the optimal exponential rates can be computed reliably from a simpler asymptotic problem posed in one space dimension.

Replacements for Fri, 10 May 24

[3]  arXiv:2307.08884 (replaced) [pdf, other]

Title: Statistics of extreme events in integrable turbulence

Authors: T. Congy, G. A. El, G. Roberti, A. Tovbis, S. Randoux, P. Suret

Comments: 13 pages, 5 figures

Subjects: Pattern Formation and Solitons (nlin.PS); Exactly Solvable and Integrable Systems (nlin.SI)

[4]  arXiv:2405.04556 (replaced) [pdf, other]

Title: Energy-based theory of autoresonance in chains of coupled damped-driven generic oscillators

Authors: Ricardo Chacón, Faustino Palmero, Pedro J. Martínez, Somnath Roy

Comments: 5 pages, 4 figures

Subjects: Chaotic Dynamics (nlin.CD); Pattern Formation and Solitons (nlin.PS)

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