Nonlocal hydrodynamic type of equations

  title={Nonlocal hydrodynamic type of equations},
  author={Metin G{\"u}rses and Aslı Pekcan and Kostyantyn Zheltukhin},
  journal={Commun. Nonlinear Sci. Numer. Simul.},

Shifted nonlocal Kundu type equations: Soliton solutions

  • A. Pekcan
  • Mathematics
    Partial Differential Equations in Applied Mathematics
  • 2022

Soliton solutions of the shifted nonlocal NLS and MKdV equations

Nonlocal KdV equations

Nonlocal $(2+1)$-dimensional Maccari equations

We obtain one-soliton solution of $(2+1)$-dimensional $3$-component Maccari system by Hirota method. Then we find local and nonlocal reductions of this system. By using the Ablowitz-Musslimani

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We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a nonstandard Lax representation. We give several examples for N=2 and N=3 containing

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Based on the completeness relation for the squared solutions of the Lax operator $L$ we show that a subset of nonlocal equations from the hierarchy of nonlocal nonlinear Schrodinger equations (NLS)

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Preliminary considerations elements of differential calculus for tensor fields the theory of Hamiltonian and bi-Hamiltonian systems lax representations of multi-Hamiltonian systems multi-Hamiltonian

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Integrable nonlocal complex mKdV equation: soliton solution and gauge equivalence

In this paper, we prove that the nonlocal complex modified Korteweg-de Vries (mKdV) equation introduced by Ablowitz and Musslimani [Nonlinearity, 29, 915-946 (2016)] is gauge equivalent to a