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 paper, the results of the interaction of counter-propagating pulses for two coupled complex cubic-quintic Ginzburg-Landau equations are discussed as they arise near the onset of a weakly inverted Hopf bifurcation.
Abstract: We discuss the results of the interaction of counter-propagating pulses for two coupled complex cubic-quintic Ginzburg–Landau equations as they arise near the onset of a weakly inverted Hopf bifurcation. As a result of the interaction of the pulses we find in 1D for periodic boundary conditions (corresponding to an annular geometry) many different possible outcomes. These are summarized in two phase diagrams using the approach velocity, v, and the real part of the cubic cross-coupling, cr, of the counter-propagating waves as variables while keeping all other parameters fixed. The novel phase diagram in the limit v ↦0, cr ↦0 turns out to be particularly rich and includes bound pairs of 2 π holes as well as zigzag bound pairs of pulses.
13 citations
TL;DR: In this paper, the cubic-quintic Gross-Pitaevskii equation was studied in one, two, and three spatial dimensions under the assumption of radial symmetry with the BEC dynamics influenced by a confining potential.
13 citations
TL;DR: In this article, it was shown that the Fermat quintic curve with 15 D4-points is projectively equivalent to the dihedral group D4 of order eight, and the number of D4 points for C equals 0, 1, 3, 5, 5 or 15.
Abstract: Let C be a nonsingular plane quintic curve over the complex number field C, and let πP : C → P be a projection from P ∈ C. Let LP be the Galois closure of the field extension C(C)/C(P) induced by πP , where C(C) and C(P) are the rational function fields of C and P, respectively. We call the point P a D4-point if the Galois group of LP /C(P) is isomorphic to the dihedral group D4 of order eight. In this paper, we prove that the number of D4-points for C equals 0, 1, 3, 5, or 15, and show that the curve with 15 D4-points is projectively equivalent to the Fermat quintic curve.
13 citations
Posted Content•
TL;DR: The additional regularity of energy solutions is established by constructing the new Lyapunov-type functional and based on this, the global well-posedness and dissipativity of the energy solutions as well as the existence of a smooth global and exponential attractors of finite Hausdorff and fractal dimension is verified.
Abstract: Dissipative wave equations with critical quintic nonlinearity and damping term involving the fractional Laplacian are considered. The additional regularity of energy solutions is established by constructing the new Lyapunov-type functional and based on this, the global well-posedness and dissipativity of the energy solutions as well as the existence of a smooth global and exponential attractors of finite Hausdorff and fractal dimension is verified.
13 citations
Journal Article•
TL;DR: In this article, a finite element method involving collocation method with quintic B-splines as basis functions have been developed to solve sixth order boundary value problems, where the basis functions are redefined into a new set of basis functions which in number match with the number of collocated points selected in the space variable domain.
Abstract: A finite element method involving collocation method with quintic B-splines as basis functions have been developed to solve sixth order boundary value problems. The sixth order and fifth order derivatives for the dependent variable are approximated by the central differences of fourth order derivatives. The basis functions are redefined into a new set of basis functions which in number match with the number of collocated points selected in the space variable domain. The proposed method is tested on several linear and non-linear boundary value problems. The solution of a non-linear boundary value problem has been obtained as the limit of a sequence of solutions of linear boundary value problems generated by quasilinearization technique. Numerical results obtained by the present method are in good agreement with the exact solutions or numerical solutions available in the literature.
13 citations