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Symmetries and integrable systems. [PDF]

Fundam Res
Lou SY, Feng BF.
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Bright and dark optical solitons for (2+1)-dimensional Schrödinger (NLS) equations in the anomalous dispersion regimes and the normal dispersive regimes

Optik, 2019
We operate the variational iteration method (VIM) for obtaining bright and dark optical solitons for (2+1)-dimensional nonlinear Schrodinger (NLS) equations, that appear in the anomalous dispersion regimes and the normal dispersive regimes respectively ...
A. Wazwaz
semanticscholar   +3 more sources

Soliton Solutions of Deformed Nonlinear Schrödinger Equations Using Ansatz Method

International Journal of Applied and Computational Mathematics, 2021
T. Mathanaranjan
semanticscholar   +3 more sources

Nonlocal M-component nonlinear Schrödinger equations: Bright solitons, energy-sharing collisions, and positons.

Physical Review E, 2020
The general set of nonlocal M-component nonlinear Schrödinger (nonlocal M-NLS) equations obeying the PT-symmetry and featuring focusing, defocusing, and mixed (focusing-defocusing) nonlinearities that has applications in nonlinear optics settings, is ...
Jiguang Rao, Jingsong He, T. Kanna, D. Mihalache   +3 more
semanticscholar   +1 more source

Defocusing Nonlinear Schrödinger Equations

, 2019
This study of Schrodinger equations with power-type nonlinearity provides a great deal of insight into other dispersive partial differential equations and geometric partial differential equations.
B. Dodson
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Breather waves, high-order rogue waves and their dynamics in the coupled nonlinear Schrödinger equations with alternate signs of nonlinearities

Europhysics letters, 2019
We consider the analytic vector breather and high-order rogue wave solutions for the coupled nonlinear Schrödinger (NLS) equations with alternate signs of nonlinearities via Darboux dressing transformation.
Wei-Qi Peng, Shou‐Fu Tian, Tian‐Tian Zhang   +2 more
semanticscholar   +1 more source

Rational soliton solutions in the parity-time-symmetric nonlocal coupled nonlinear Schrödinger equations

Communications in nonlinear science & numerical simulation, 2018
In this paper, via the Darboux transformation (DT) method, we study the nonlocal coupled nonlinear Schrodinger (NLS) equations with parity-time ( PT )-symmetric nonlinearities.
Hai-Qiang Zhang, Min Gao
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Blow-up criteria for fractional nonlinear Schrödinger equations

Nonlinear Analysis: Real World Applications, 2018
We consider the focusing fractional nonlinear Schr\"odinger equation \[ i\partial_t u - (-\Delta)^s u = -|u|^\alpha u, \quad (t,x) \in \mathbb{R}^+ \times \mathbb{R}^d, \] where $s \in (1/2,1)$ and $\alpha>0$.
Van Duong Dinh
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The virial theorem and ground state energy estimates of nonlinear Schrödinger equations in $$\mathbb {R}^2$$R2 with square root and saturable nonlinearities in nonlinear optics

, 2016
The virial theorem is a nice property for the linear Schrödinger equation in atomic and molecular physics as it gives an elegant ratio between the kinetic and potential energies and is useful in assessing the quality of numerically computed eigenvalues ...
Tai-Chia Lin, M. Belić, M. Petrović, H. Hajaiej, Goong Chen   +4 more
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Multi-component Nonlinear Schrödinger Equations with Nonzero Boundary Conditions: Higher-Order Vector Peregrine Solitons and Asymptotic Estimates

Journal of nonlinear science, 2021
Guoqiang Zhang, Liming Ling, Zhenya Yan
semanticscholar   +1 more source