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Soliton solution and gauge equivalence for an integrable nonlocal complex modified Korteweg-de Vries equation
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In this paper, an integrable nonlocal complex modified Korteweg-de Vries (mKdV) equation introduced by Ablowitz and Musslimani is shown to be gauge equivalent to a spin-like model.Abstract:
In this paper, we prove that an integrable nonlocal complex modified Korteweg-de Vries (mKdV) equation introduced by Ablowitz and Musslimani [Nonlinearity 29, 915–946 (2016)] is gauge equivalent to a spin-like model. From the gauge equivalence, one can see that there exists significant difference between the nonlocal complex mKdV equation and the classical complex mKdV equation. Through constructing the Darboux transformation for nonlocal complex mKdV equation, a variety of exact solutions including dark soliton, W-type soliton, M-type soliton, and periodic solutions are derived.read more
Citations
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Nonlocal nonlinear Schrödinger equations and their soliton solutions
Metin Gürses,Aslı Pekcan +1 more
TL;DR: In this article, the standard and non-local nonlinear Schrodinger (NLS) equations obtained from the coupled NLS system of equations (AKNS) were studied by using the Hirota bilinear method.
Journal ArticleDOI
General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions
TL;DR: In this article, general soliton solutions to nonlinear Schrodinger (NLS) with Parity (PT)-symmetry for both zero and nonzero boundary conditions are obtained.
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General N-solitons and their dynamics in several nonlocal nonlinear Schrödinger equations
TL;DR: In this paper, general N-solitons in three recently-proposed nonlocal nonlinear Schrodinger equations are presented, including reverse-space, reverse-time, and reversespace-time nonlinear solitons, which are nonlocal reductions of the Ablowitz-Kaup-Newell-Segur hierarchy.
Journal ArticleDOI
General soliton solution to a nonlocal nonlinear Schr\"odinger equation with zero and nonzero boundary conditions
TL;DR: In this paper, general soliton solutions to nonlinear Schrodinger (NLS) equations with PT-symmetry for both zero and nonzero boundary conditions are considered via the combination of Hirota's bilinear method and the Kadomtsev-Petviashvili (KP) hierarchy reduction method.
Journal ArticleDOI
Nonlocal Nonlinear Schr\"odinger Equations and Their Soliton Solutions
Metin Gürses,Aslı Pekcan +1 more
TL;DR: In this paper, the standard and non-local nonlinear Schrodinger (NLS) equations obtained from the coupled NLS system of equations (AKNS) were studied by using the Hirota bilinear method.
References
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Integrable nonlocal nonlinear Schrödinger equation.
TL;DR: A new integrable nonlocal nonlinear Schrödinger equation is introduced that possesses a Lax pair and an infinite number of conservation laws and is PT symmetric.
A numerical and theoretical study of certain nonlinear wave phenomena
Bengt Fornberg,G. B. Whitham +1 more
TL;DR: In this article, an efficient numerical method is developed for solving nonlinear wave equations typified by the Korteweg-de Vries equation and its generalizations, using a pseudospectral (Fourier transform) treatment of the space dependence together with a leap-frog scheme in time.
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A Numerical and Theoretical Study of Certain Nonlinear Wave Phenomena
Bengt Fornberg,G. B. Whitham +1 more
TL;DR: An efficient numerical method is developed for solving nonlinear wave equations typified by the Korteweg-de Vries equation and its generalizations using a pseudospectral (Fourier transform) treatment of the space dependence together with a leap-frog scheme in time.
Journal ArticleDOI
Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation
TL;DR: In this paper, a detailed study of the inverse scattering transform of the non-local nonlinear Schrodinger (NLS) equation is carried out and key symmetries of the eigenfunctions and scattering data and conserved quantities are obtained.
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Continuum spin system as an exactly solvable dynamical system
TL;DR: In this paper, it was shown that the one-dimensional classical spins with nearest neighbor Heisenberg interaction is an exactly solvable system and its dynamics describable by the nonlinear Schrodinger equation.