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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 studied the number of limit cycles of a near-Hamiltonian system having Z4-equivariant quintic perturbations and found that the perturbed system can have 28 limit cycles, and its location is also given.
Abstract: In this paper, we study the number of limit cycles of a near-Hamiltonian system having Z4-equivariant quintic perturbations. Using the methods of Hopf and heteroclinic bifurcation theory, we find that the perturbed system can have 28 limit cycles, and its location is also given. The main result can be used to improve the lower bound of the maximal number of limit cycles for some polynomial systems in a previous work, which is the main motivation of the present paper.
6 citations
6 citations
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TL;DR: In this paper, a detailed study of attractors for measure driven quintic damped wave equations with periodic boundary conditions is presented. And the existence of uniform attractors in a weak or strong topology in the energy phase space, the possibility to present them as a union of all complete trajectories, further regularity, etc.
Abstract: We give a detailed study of attractors for measure driven quintic damped wave equations with periodic boundary conditions. This includes uniform energy-to-Strichartz estimates, the existence of uniform attractors in a weak or strong topology in the energy phase space, the possibility to present them as a union of all complete trajectories, further regularity, etc.
6 citations
TL;DR: In this article, a geo-numerical approach for classifying fixed points of the set of ODEs that represent the reduced model of the cubic-quintic complex Ginzburg-Landau equation (CQ CGL) in a two parameter plane is presented.
6 citations
TL;DR: In this paper, exact solitary wave solutions of the one-dimensional quintic complex Ginzburg-Landau equation are obtained using a method derived from the Painlev\'e test for integrability.
Abstract: Exact solitary wave solutions of the one-dimensional quintic complex Ginzburg-Landau equation are obtained using a method derived from the Painlev\'e test for integrability. These solutions are expressed in terms of hyperbolic functions, and include the pulses and fronts found by van Saarloos and Hohenberg. We also find previously unknown sources and sinks. The emphasis is put on the systematic character of the method which breaks away from approaches involving somewhat ad hoc Ans\"atze.
6 citations