Topic
Quintic function
About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.
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TL;DR: In this article, the authors used the self-similarity transformation to find analytical spatial bright and dark selfsimilar solitons of the generalized (2+1)-dimensional quintic nonlinear Schrodinger equation with varying diffraction, nonlinearity, and gain.
Abstract: Using the self-similarity transformation, we find analytical spatial bright and dark self-similar solitons, i.e., the similaritons, of the generalized (2+1)-dimensional quintic nonlinear Schrodinger equation with varying diffraction, nonlinearity, and gain. Characteristic examples with physically relevant behavior of these similaritons are studied, and the stability of these solutions is verified with numerical integration.
24 citations
TL;DR: In this paper, a method based on the identification of coefficients of hyperbolic functions for the construction of the soliton solutions of the cubic and quintic nonlinear Ginzburg-Landau equations was proposed.
Abstract: We apply a method based on the identification of coefficients of hyperbolic functions for the construction of the soliton solutions of the cubic and quintic nonlinear Ginzburg–Landau equations. This effective method improves the solution when the nonlinearity increases.
24 citations
TL;DR: In this article, a rigorous approach based on the Whitham modulation theory was employed to investigate dispersive shock waves arising in a high-order nonlinear Schr¨ odinger equation with competing cubic and quintic nonlinear responses.
Abstract: By employing a rigorous approach based on the Whitham modulation theory, we investigate dispersive shock waves arising in a high-order nonlinear Schr¨ odinger equation with competing cubic and quintic nonlinear responses. This model finds important applications in both nonlinear optics and Bose-Einstein condensates. Our theory predicts the formation of dispersive shocks with totally controllable properties, encompassing both steering and compression effects. Numerical simulations confirm these results perfectly. Quite remarkably, shock tuning can be achieved in the regime of a very small high order, i.e. quintic, nonlinearity.
24 citations
TL;DR: In this article, the structure of function fields of plane curves was studied and the number of Galois points on singular plane quartic curves was determined, and the defining equations when the curve has a Galois point were given.
24 citations
TL;DR: In this paper, a new transformation v = 4 ( ln f ) x x that can formulate a quintic linear equation and a pair of Hirota's bilinear equations for the (2 − 1)-dimensional Sawada-Kotera (2DSK) Eq. (2) is reported.
24 citations