Now showing items 1-17 of 17

    • 2 + 1 KdV(N) equations 

      Gürses, M.; Pekcan, A. (American Institute of Physics, 2011)
      We present some nonlinear partial differential equations in 2 + 1-dimensions derived from the KdV equation and its symmetries. We show that all these equations have the same 3-soliton solution structures. The only difference ...
    • (2+1)-dimensional local and nonlocal reductions of the negative AKNS system: soliton solutions 

      Gürses, Metin; Pekcan, A. (Elsevier, 2018)
      Wefirstconstructa(2+1)dimensionalnegativeAKNShierarchyandthenwegiveallpossiblelocaland(discrete)nonlocalreductionsoftheseequations.WefindHirotabilinearformsofthenegativeAKNShierarchyandgiveone-andtwo-solitonsolutions.Byu ...
    • Characteristic Lie algebra and classification of semidiscrete models 

      Habibullin, I. T.; Pekcan, A. (Springer New York LLC, 2007)
      We study characteristic Lie algebras of semi-discrete chains and attempt to use this notion to classify Darboux-integrable chains. © Springer Science+Business Media, Inc. 2007.
    • Complete list of Darboux integrable chains of the form t 1 x = t x + d ( t, t 1 ) 

      Habibullin, I.; Zheltukhina, N.; Pekcan, A. (2009)
      We study differential-difference equation (d/dx) t (n+1,x) =f (t (n,x),t (n+1,x), (d/dx) t (n,x)) with unknown t (n,x) depending on continuous and discrete variables x and n. Equation of such kind is called Darboux integrable, ...
    • Discrete symmetries and nonlocal reductions 

      Gürses, Metin; Pekcan, A.; Zheltukhin, K. (Elsevier, 2020)
      We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.
    • Integrable nonlocal reductions 

      Gürses, Metin; Pekcan, A. (Springer New York LLC, 2018)
      We present some nonlocal integrable systems by using the Ablowitz-Musslimani nonlocal reductions. We first present all possible nonlocal reductions of nonlinear Schrödinger (NLS) and modified Korteweg-de Vries (mKdV) ...
    • Nonlocal hydrodynamic type of equations 

      Gürses, Metin; Pekcan, A.; Zheltukhin, K. (Elsevier, 2020-03-01)
      We show that the integrable equations of hydrodynamic type admit nonlocal reductions. We first construct such reductions for a general Lax equation and then give several examples. The reduced nonlocal equations are of ...
    • Nonlocal KdV equations 

      Gürses, Metin; Pekcan, A. (Elsevier, 2020)
      Writing the Hirota-Satsuma (HS) system of equations in a symmetrical form we find its local and new nonlocal reductions. It turns out that all reductions of the HS system are Korteweg-de Vries (KdV), complex KdV, and new ...
    • Nonlocal modified KdV equations and their soliton solutions by Hirota Method 

      Gürses, Metin; Pekcan, A. (Elsevier, 2019)
      We study the nonlocal modified Korteweg–de Vries (mKdV) equations obtained from AKNS scheme by Ablowitz–Musslimani type nonlocal reductions. We first find soliton solutions of the coupled mKdV system by using the Hirota ...
    • Nonlocal nonlinear Schrödinger equations and their soliton solutions 

      Gürses, Metin; Pekcan, A. (American Institute of Physics, 2018-05-04)
      We study standard and nonlocal nonlinear Schrödinger (NLS) equations obtained from the coupled NLS system of equations (Ablowitz-Kaup-Newell-Segur (AKNS) equations) by using standard and nonlocal reductions, respectively. ...
    • On the classification of Darboux integrable chains 

      Habibullin, I.; Zheltukhina, N.; Pekcan, A. (American Institute of Physics, 2008)
      We study differential-difference equation (d/dx) t (n+1,x) =f (t (n,x),t (n+1,x), (d/dx) t (n,x)) with unknown t (n,x) depending on continuous and discrete variables x and n. Equation of such kind is called Darboux integrable, ...
    • The relationship between destination performance, overall satisfaction, and behavioral intention for distinct segments 

      Baloglu, S.; Pekcan, A.; Chen, S.; Santos, J. (Routledge, 2004)
      Destination performance, visitor satisfaction, and favorable future behavior of visitors are key determinants of destination competitiveness. Most empirical work, assuming that overall tourist population is homogenous, ...
    • Solutions of the extended Kadomtsev-Petviashvili-Boussinesq equation by the Hirota direct method 

      Pekcan, A. (Taylor & Francis Asia Pacific (Singapore), 2009)
      We show that we can apply the Hirota direct method to some non-integrable equations. For this purpose, we consider the extended Kadomtsev-Petviashvili- Boussinesq (eKPBo) equation with M variable which is (uxxx-6uu x)x + ...
    • Superposition of the coupled NLS and MKdV systems 

      Gürses, Metin; Pekcan, A. (Elsevier, 2019)
      Superpositions of hierarchies of integrable equations are also integrable. The superposed equations, such as the Hirota equations in the AKNS hierarchy, cannot be considered as new integrable equations. Furthermore if ...
    • Traveling wave solutions of degenerate coupled multi-KdV equations 

      Gürses M.; Pekcan, A. (American Institute of Physics, 2016)
      Traveling wave solutions of degenerate coupled ℓ-KdV equations are studied. Due to symmetry reduction these equations reduce to one ordinary differential equation (ODE), i.e., (f′)2 = Pn(f) where Pn(f) is a polynomial ...
    • Travelling wave solution of degenerate coupled KdV equations 

      Gürses M.; Pekcan, A. (A I P Publishing, 2014)
      We give a detailed study of the traveling wave solutions of (l = 2) Kaup-Boussinesq type of coupled KdV equations. Depending upon the zeros of a fourth degree polynomial, we have cases where there exist no nontrivial real ...
    • Uniqueness of the Kadomtsev-Petviashvili and Boussinesq Equations 

      Ma W.-X.; Pekcan, A. (2011)
      The Kadomtsev-Petviashvili and Boussinesq equations (u xxx - 6uu x)x - ut x ± uyy = 0, (u xxx - 6uu x)x + u xx ± u tt = 0, are completely integrable, and in particular, they possess the three-soliton solution. This article ...