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Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions
Guoqiang Zhang,Zhenya Yan +1 more
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TLDR
In this article, a systematical inverse scattering transform for both focusing and defocusing nonlocal (reverse-space-time) modified Korteweg-de Vries (mKdV) equations with non-zero boundary conditions (NZBCs) at infinity is presented.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 2020-01-15. It has received 85 citations till now. The article focuses on the topics: Inverse scattering transform & Inverse scattering problem.read more
Citations
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The Derivative Nonlinear Schrödinger Equation with Zero/Nonzero Boundary Conditions: Inverse Scattering Transforms and N-Double-Pole Solutions
Guoqiang Zhang,Zhenya Yan +1 more
TL;DR: A rigorous theory of the inverse scattering transforms (ISTs) for the derivative nonlinear Schrodinger (DNLS) equation with both zero boundary conditions and nonzero boundary conditions at infinity and double zeros of analytical scattering coefficients is reported.
Journal ArticleDOI
Focusing and defocusing Hirota equations with non-zero boundary conditions: Inverse scattering transforms and soliton solutions
TL;DR: The inverse scattering transforms and soliton solutions of both focusing and defocusing Hirota equations with non-zero boundary conditions (NZBCs) are investigated and obtained solutions are useful to explain the related nonlinear wave phenomena.
Journal ArticleDOI
Focusing and defocusing mKdV equations with nonzero boundary conditions: Inverse scattering transforms and soliton interactions
Guoqiang Zhang,Zhenya Yan +1 more
TL;DR: In this paper, the inverse scattering transforms with matrix Riemann-Hilbert problems for both focusing and defocusing modified Korteweg-de Vries (mKdV) equations with non-zero boundary conditions (NZBCs) at infinity systematically were explored.
Journal ArticleDOI
Multi-place physics and multi-place nonlocal systems
TL;DR: In this article, the authors mainly review the recent progress on two-place nonlocal systems (Alice-Bob systems) and four-place NLS models and show that all the known powerful methods used in local systems can be applied to nonlocal cases.
Journal ArticleDOI
Inverse scattering and N-triple-pole soliton and breather solutions of the focusing nonlinear Schrödinger hierarchy with nonzero boundary conditions
Weifang Weng,Zhenya Yan +1 more
TL;DR: Based on the matrix Riemann-Hilbert problem, this article presented the inverse scattering transform for the focusing nonlinear Schrodinger (NLS) equation with nonzero boundary conditions (NZBCs) at infinity and triple zeros of analytical scattering coefficients.
References
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Journal ArticleDOI
Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
TL;DR: The condition of self-adjointness as discussed by the authors ensures that the eigenvalues of a Hamiltonian are real and bounded below, replacing this condition by the weaker condition of $\mathrm{PT}$ symmetry, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive.
Book
Solitons, Nonlinear Evolution Equations and Inverse Scattering
M. A. Ablowitz,Peter A. Clarkson +1 more
TL;DR: In this article, the authors bring together several aspects of soliton theory currently only available in research papers, including inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multidimensional space, and the ∂ method.
Journal ArticleDOI
Method for solving the Korteweg-deVries equation
TL;DR: In this paper, a method for solving the initial value problem of the Korteweg-deVries equation is presented which is applicable to initial data that approach a constant sufficiently rapidly as
Journal Article
Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media
Journal ArticleDOI
The Inverse scattering transform fourier analysis for nonlinear problems
TL;DR: In this article, a systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering, where the form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro-differential operator.
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