Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · nlin/0103014

One- and two-dimensional solitons in saturable media

Boris V. Gisin·Boris A. Malomed
View original source ↗Read source document ↗Export metadata ↓

Abstract

Very narrow spatial bright solitons in (1+1)D and (2+1)D versions of cubic-quintic and full saturable models are studied, starting from the full system of the Maxwell's equations, rather than from the paraxial (NLS) approximation. For the solitons with both TE and TM polarizations, it is shown that there always exists a finite minimum width, and they cease to exist at a critical value of the propagation constant, at which their width diverges. Full similarity of the results obtained for both nonlinearities suggests that the same general conclusions apply to narrow solitons in any non-Kerr model.

Explore related subjects

nlin.PS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Boris V. Gisin, Boris A. Malomed. 2001-03-13. One- and two-dimensional solitons in saturable media. https://doi.org/10.1364/josab.18.001356

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Duck hunting with quantum mechanics

We bridge two sides of singular perturbation theory: the classical theory of slow-fast systems and the semi-classical approach to quantum mechanical systems. For a specific but physically important class of dynamical systems, we show that purely classical and exotic objects, so-called canard solutions, are shadows of instantons in the corresponding quantum system. We demonstrate that canard solutions exist in a domain of parameter space whose boundaries are determined by an instanton action. We illustrate our statements analytically for the relevant example, the overdamped Josephson junction, and confirm them numerically. For the Josephson junction, the canard window is the exponentially narrow gap between consecutive Shapiro steps.

nlin.PS↗
arXiv2026

Rolls and Snaking in a Swift-Hohenberg Equation with Non-smooth Nonlinearity

We study rolls and homoclinic snaking in a variation of the one-dimensional Swift-Hohenberg equation, whose standard forms are prototypical order-parameter models for pattern formation in the sciences. Motivated by classes of differential equation models that involve continuous non-smooth low order nonlinear terms, we replace the standard quadratic-cubic nonlinearity by $ν|u|^α-u^3$, $α\in [1,2]$ with $ν> 0$. In the vicinity of zero, for $α<2$ this nonlinearity falls outside the scope of classical Taylor expansion and bifurcation analysis. Our partially analytical and partially numerical results highlight that the non-smooth term modifies the criticality of pattern-forming bifurcations and alters the associated branches of solutions. In particular, $α\in(1,2)$ implies subcriticality of roll bifurcations for any $ν>0$. At $α=1$ differentiability is lost, which has a strong impact on the bifurcations of sign-changing rolls including the disappearance of homoclinic snaking. Homoclinic snaking thus emerges non-smoothly as $α$ increases from $α=1$, and persists when retaining an additional, e.g., quadratic term.

nlin.PS↗