Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
Browse
3 results
Search Results
Conference Object Citation - WoS: 1Resonant Dispersive Benney and Broer-Kaup Systems in 2+1 Dimensions(IOP Publishing Ltd., 2014) Lee, Jyh Hao; Pashaev, OktayWe represent the Benney system of dispersionless hydrodynamic equations as NLS type infinite system of equations with quantum potential. We show that negative dispersive deformation of this system is an integrable system including vector generalization of Resonant NLS and 2+1 dimensional nonlocal Resonant NLS. We obtain bilinear form and soliton solutions in these systems and find the resonant character of soliton interaction. Equivalent vector Broer-Kaup system and non-local 2+1 dimensional nonlocal Broer-Kaup equation are constructed.Article Citation - WoS: 26Citation - Scopus: 27Analytic Solutions To Nonlinear Differential-Difference Equations by Means of the Extended (g'/g)-expansion Method(IOP Publishing Ltd., 2010) Aslan, İsmailIn this paper, a discrete extension of the (G′/G)-expansion method is applied to a relativistic Toda lattice system and a discrete nonlinear Schrödinger equation in order to obtain discrete traveling wave solutions. Closed form solutions with more arbitrary parameters, which reduce to solitary and periodic waves, are exhibited. New rational solutions are also obtained. The method is straightforward and concise, and its applications in physical sciences are promising. © 2010 IOP Publishing Ltd.Article Citation - WoS: 12Citation - Scopus: 11Q-Analog of Shock Soliton Solution(IOP Publishing Ltd., 2010) Nalcı, Şengül; Pashaev, OktayBased on Jackson's q-exponential function, we introduce a q-analog of Hermite and Kampe de Feriet polynomials. It allows us to introduce and solve the q-heat equation in terms of q-Kampe de Feriet polynomials with arbitrary number of moving zeros, and to find an operator solution for the initial value problem. By the q-analog of Cole-Hopf transformation we find a new q-Burgers-type nonlinear heat equation with cubic nonlinearity, such that in the q → 1 limit it reduces to the standard Burgers equation. We construct exact solutions for the q-Burgers equation in the form of moving poles, singular and regular q-shock soliton solutions. A novel, self-similarity property of the stationary q-shock soliton solution is found. © 2010 IOP Publishing Ltd.