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Öğe Stability of periodic waves for the defocusing fractional cubic nonlinear Schrödinger equation(Elsevier B.V., 2024) Borluk, Handan; Natali, Fábio; Muslu, Gülçin MihriyeIn this paper, we determine the spectral instability of periodic odd waves for the defocusing fractional cubic nonlinear Schrödinger equation. Our approach is based on periodic perturbations that have the same period as the standing wave solution, and we construct real periodic waves by minimizing a suitable constrained problem. The odd solution generates three negative simple eigenvalues for the associated linearized operator, and we obtain all this spectral information by using tools related to the oscillation theorem for fractional Hill operators. Newton's iteration method is presented to generate the odd periodic standing wave solutions and numerical results have been used to apply the spectral stability theory via Krein signature as established in Kapitula et al. (2004) and Kapitula et al. (2005).Öğe Positive solutions of sublinear Emden-Fowler equation(Springer Wien, 2023) Aslanov, Afgan; Aslanova, GünayWe consider the existence of a positive solution to the sublinear Emden-Fowler equations. An existence of nonoscillating solution to the sublinear Emden-Fowler equations with right hand side is also presented.Öğe On the Kadomtsev–Petviashvili equation with double-power nonlinearities(Elsevier B.V., 2024) Esfahani, Amin; Levandosky, Steven; Muslu, Gülçin MihriyeIn this paper, we study the generalized KP equation with double-power nonlinearities. Our investigation covers various aspects, including the existence of solitary waves, their nonlinear stability, and instability. Notably, we address a broader class of nonlinearities represented by ?1|u|pu+?2|u|pu, with p1>p2, encompassing cases where ?1>0 and ?1<0
