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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 examined the combined effects of cubic and quintic terms of the long-range type in the dynamics of a double well potential and systematically developed two cubic?quintic ordinary differential equations.
Abstract: In the present work, we examine the combined effects of cubic and quintic terms of the long-range type in the dynamics of a double well potential. Employing a two-mode approximation, we systematically develop two cubic?quintic ordinary differential equations and assess the contributions of the long-range interactions in each of the relevant prefactors, gauging how to simplify the ensuing dynamical system. Finally, we obtain a reduced canonical description for the conjugate variables of relative population imbalance and relative phase between the two wells and proceed to a dynamical systems analysis of the resulting pair of ordinary differential equations. While in the case of cubic and quintic interactions of the same kind (e.g. both attractive or both repulsive), only a symmetry-breaking bifurcation can be identified, a remarkable effect that emerges e.g. in the setting of repulsive cubic but attractive quintic interactions is a ?symmetry-restoring? bifurcation. Namely, in addition to the supercritical pitchfork that leads to a spontaneous symmetry breaking of the antisymmetric state, there is a subcritical pitchfork that eventually reunites the asymmetric daughter branch with the antisymmetric parent one. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. The model is argued to be of physical relevance, especially so in the context of optical thermal media.
6 citations
6 citations
TL;DR: Monotonicity-preserving interpolation is generalized to direction-consistent interpolation and the balanced tangent vectors are presented and proved to be direction- Consistent tangent vector.
6 citations
TL;DR: In this article, a more general nonlocal integrable nonlinear Schrodinger equation with nonlocal cubic and quintic nonlinearities in addition to external potential was proposed, where similarity transformation and Lax-pair method were employed to achieve integrability of the model and then suitably exploited the Darboux transformation approach to generate more general solitonic solutions.
6 citations
TL;DR: In this paper, the exact solutions of variable coefficient cubic-quintic nonlinear Schrodinger equation with an external potential were obtained by constructing appropriate transformations and an extended elliptic sub-equation approach.
Abstract: By constructing appropriate transformations and an extended elliptic sub-equation approach, we find some exact solutions of variable coefficient cubic-quintic nonlinear Schrodinger equation with an external potential, which include bell and kink profile solitary wave solutions, singular solutions, triangular periodic wave solutions and so on.
6 citations