Nonlocal hydrodynamic type of equations

@article{Grses2019NonlocalHT,
  title={Nonlocal hydrodynamic type of equations},
  author={Metin G{\"u}rses and Aslı Pekcan and Kostyantyn Zheltukhin},
  journal={Commun. Nonlinear Sci. Numer. Simul.},
  year={2019},
  volume={85},
  pages={105242}
}

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

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Discrete symmetries and nonlocal reductions

References

SHOWING 1-10 OF 46 REFERENCES

Recursion operators of some equations of hydrodynamic type

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

Nonlocal Super Integrable Equations

We present nonlocal integrable reductions of super AKNS coupled equations. By the use of nonlocal reductions of Ablowitz and Musslimani we find new super integrable equations. In particular we

Integrable nonlocal nonlinear Schrödinger equation.

A new integrable nonlocal nonlinear Schrödinger equation is introduced. It possesses a Lax pair and an infinite number of conservation laws and is PT symmetric. The inverse scattering transform and

Classical r-Matrices and Compatible Poisson Structures for Lax Equations on Poisson Algebras

Abstract:Given a classical r-matrix on a Poisson algebra, we show how to construct a natural family of compatible Poisson structures for the Hamiltonian formulation of Lax equations. Examples for

Complete integrability of Nonlocal Nonlinear Schr\"odinger equation

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)

Multi-Hamiltonian Theory of Dynamical Systems

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

Introduction to classical integrable systems

1. Introduction 2. Integrable dynamical systems 3. Synopsis of integrable systems 4. Algebraic methods 5. Analytical methods 6. The closed Toda chain 7. The Calogero-Moser model 8. Isomonodromic

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