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Journal articles on the topic 'Nonlinear Solitons Schrödinger equation'

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Published: 4 June 2021
Last updated: 21 February 2023

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1

E. Zayed, Elsayed M. "On solving the nonlinear Biswas-Milovic equation with dual-power law nonlinearity using the extended tanh-function method." JOURNAL OF ADVANCES IN PHYSICS 11, no. 2 (2015): 3001–12. http://dx.doi.org/10.24297/jap.v11i2.518.

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In this article, we apply the extended tanh-function method to …nd the exact traveling wave solutions of the nonlinear Biswas-Milovic equation (BME), which describes the prop-agation of solitons through optical …bers for trans-continental and trans-oceanic distances. This equation is a generalized version of the nonlinear Schrödinger equation with dual-power law nonlinearity. With the aid of computer algebraic system Maple, both constant and time-dependent coe¢ cients of BME are discussed. Comparison between our new results and the well-known results is given. The given method in this
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2

Stiller, Olaf, Stefan Popp, and Lorenz Kramer. "From dark solitons in the defocusing nonlinear Schro¨dinger to holes in the complex Ginzburg-Landau equation." Physica D: Nonlinear Phenomena 84, no. 3-4 (1995): 424–36. http://dx.doi.org/10.1016/0167-2789(95)00071-b.

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3

Kotlyarov, V. P., and E. Ya Khruslov. "Solitons of the nonlinear Schr�dinger equation generated by the continuum." Theoretical and Mathematical Physics 68, no. 2 (1986): 751–61. http://dx.doi.org/10.1007/bf01035537.

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4

Qian Cun, Wang Liang-Liang, and Zhang Jie-Fang. "Solitons of nonlinear Schrödinger equation withvariable-coefficients and interaction." Acta Physica Sinica 60, no. 6 (2011): 064214. http://dx.doi.org/10.7498/aps.60.064214.

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5

Fedele, R., H. Schamel, V. I. Karpman, and P. K. Shukla. "Envelope solitons of nonlinear Schr dinger equation with an anti-cubic nonlinearity." Journal of Physics A: Mathematical and General 36, no. 4 (2003): 1169–73. http://dx.doi.org/10.1088/0305-4470/36/4/322.

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6

Karpman, V. I. "Radiation of Solitons Described by a Higher-Order Nonlinear Schr?dinger Equation." Physica Scripta T82, no. 1 (1999): 44. http://dx.doi.org/10.1238/physica.topical.082a00044.

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7

Tchaho, Clovis Taki Djeumen, Hugues Martial Omanda, Gaston N’tchayi Mbourou, Jean Roger Bogning, and Timoléon Crépin Kofané. "Hybrid Dispersive Optical Solitons in Nonlinear Cubic-Quintic-Septic Schrödinger Equation." Optics and Photonics Journal 11, no. 02 (2021): 23–49. http://dx.doi.org/10.4236/opj.2021.112003.

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8

Erofeev, V. I., and A. V. Leontieva. "QUASIHARMONIC BENDING WAVE, DISTRIBUTING IN THE BALK OF TIMOSHENKO, LYING ON A NONLINEAR ELASTIC BASE." Problems of strenght and plasticity 83, no. 1 (2021): 61–75. http://dx.doi.org/10.32326/1814-9146-2021-83-1-61-75.

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In this paper, we consider the modulation instability of a quasiharmonic flexural wave propagating in a homogeneous beam fixed on a nonlinear elastic foundation. The dynamic behavior of the beam is determined by Timoshenko's theory. Timoshenko's model, refining the technical theory of rod bending, assumes that the crosssections remain flat, but not perpendicular to the deformable midline of the rod; normal stresses on sites parallel to the axis are zero; the inertial components associated with the rotation of the cross sections are taken into account. The uniqueness of the model lies in the fa
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9

Chen, Weikang. "Vortex Solitons for a Class of Schrödinger Equation with Square Root Nonlinear Term." Advances in Pure Mathematics 10, no. 04 (2020): 174–80. http://dx.doi.org/10.4236/apm.2020.104011.

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10

Chen, Yu, Iman Tavakkolnia, Alex Alvarado, and Majid Safari. "On the Capacity of Amplitude Modulated Soliton Communication over Long Haul Fibers." Entropy 22, no. 8 (2020): 899. http://dx.doi.org/10.3390/e22080899.

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The capacity limits of fiber-optic communication systems in the nonlinear regime are not yet well understood. In this paper, we study the capacity of amplitude modulated first-order soliton transmission, defined as the maximum of the so-called time-scaled mutual information. Such definition allows us to directly incorporate the dependence of soliton pulse width to its amplitude into capacity formulation. The commonly used memoryless channel model based on noncentral chi-squared distribution is initially considered. Applying a variance normalizing transform, this channel is approximated by a un
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11

Changfu Liu, Min Chen, Ping Zhou, and Longwei Chen. "BI-SOLITONS, BREATHER SOLUTION FAMILY AND ROGUE WAVES FOR THE (2+1)-DIMENSIONAL NONLINEAR SCHRÖDINGER EQUATION." Journal of Applied Analysis & Computation 6, no. 2 (2016): 367–75. http://dx.doi.org/10.11948/2016028.

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12

Kotlyarov, V. P. "Influence of a double continuous spectrum of the Dirac operator on the asymptotic solitons of a nonlinear Schr�dinger equation." Mathematical Notes of the Academy of Sciences of the USSR 49, no. 2 (1991): 172–80. http://dx.doi.org/10.1007/bf01137548.

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13

Wen-jing FANG, 房文静, та 宋丽军 Li-jun SONG. "广义耦合非线性薛定谔方程的N-孤子解". Acta Sinica Quantum Optica 26, № 3 (2020): 291. http://dx.doi.org/10.3788/jqo20202603.0601.

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14

Li-jun SONG, 宋丽军, та 徐晓雅 Xiao-ya XU. "广义耦合非线性薛定谔方程的4-暗孤子解". Acta Sinica Quantum Optica 26, № 2 (2020): 172. http://dx.doi.org/10.3788/jqo20202602.0602.

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15

Li-jun SONG, 宋丽军, та 房文静 Wen-jing FANG. "高阶效应对耦合非线性薛定谔方程N-孤子解传输特性的影响". Acta Sinica Quantum Optica 28, № 1 (2022): 18. http://dx.doi.org/10.3788/jqo20222801.0601.

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16

Popowicz, Ziemowit. "The extended supersymmetrization of the nonlinear Schro¨dinger equation." Physics Letters A 194, no. 5-6 (1994): 375–79. http://dx.doi.org/10.1016/0375-9601(94)91296-3.

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17

WEI Jian-ping, 魏建平, 王俊 WANG Jun, 江兴方 JIANG Xing-fang, and 唐斌 TANG Bin. "Characteristics for the Soliton Based on Nonlinear Schrdinger Equation." ACTA PHOTONICA SINICA 42, no. 6 (2013): 674–78. http://dx.doi.org/10.3788/gzxb20134206.0674.

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18

Vysloukh, V. A., and I. V. Cherednik. "On restricted N-soliton solutions of the nonlinear Schr�dinger equation." Theoretical and Mathematical Physics 71, no. 1 (1987): 346–51. http://dx.doi.org/10.1007/bf01029093.

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19

Jia-Ren, Yan, Pan Liu-Xian, and Lu Jing. "A certain critical two-soliton solution of the nonlinear Schr dinger equation." Chinese Physics 13, no. 4 (2004): 441–44. http://dx.doi.org/10.1088/1009-1963/13/4/004.

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20

金, 玲玉. "The Existence of Global Solution of Fractional Nonlinear SchrO¨dinger Equation." Dynamical Systems and Control 04, no. 04 (2015): 85–92. http://dx.doi.org/10.12677/dsc.2015.44011.

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21

Vysloukh, V. A., and I. V. Cherednik. "Many-soliton components of solutions of nonlinear Schr�dinger equation with perturbing term." Theoretical and Mathematical Physics 78, no. 1 (1989): 24–31. http://dx.doi.org/10.1007/bf01016913.

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22

Steudel, H. "The hierarchy of multi-soliton solutions of the derivative nonlinear Schr dinger equation." Journal of Physics A: Mathematical and General 36, no. 7 (2003): 1931–46. http://dx.doi.org/10.1088/0305-4470/36/7/309.

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23

Feng, Pang Xiao. "The build of nonlinear quantum mechancs and variations of feature of microscopic particles as well as their experimental affirmation." JOURNAL OF ADVANCES IN PHYSICS 5, no. 3 (2014): 871–981. http://dx.doi.org/10.24297/jap.v5i3.1927.

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We establish the nonlinear quantum mechanics due to difficulties and problems of original quantum mechanics, in which microscopic particles have only a wave feature, not corpuscle feature, which are completely not consistent with experimental results and traditional concept of particle. In this theory the microscopic particles are no longer a wave, but localized and have a wave-corpuscle duality, which are represented by the following facts, the solutions of dynamic equation describing the particles have a wave-corpuscle duality, namely it consists of a mass center with constant size and carri
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24

Zhou Yu, 周昱, 张远 Zhang Yuan, 王颖 Wang Ying, 赵明琳 Zhao Minglin, and 闫东广 Yan Donguang. "Dark Soliton Properties of Nonlinear Schr?dinger Equation with (2n+1)-th Order Nonlinearity." Acta Optica Sinica 40, no. 9 (2020): 0927001. http://dx.doi.org/10.3788/aos202040.0927001.

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25

XU Xiao-ya, 徐晓雅, and 宋丽军 SONG Li-jun. "Two-soliton Solution and Its Interaction of Coupled Nonlinear Schrdinger Equation with Variable Coefficients." Acta Sinica Quantum Optica 25, no. 2 (2019): 187–96. http://dx.doi.org/10.3788/jqo20192502.0601.

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26

Zong Feng-De, Dai Chao-Qing, Yang Qin, and Zhang Jie-Fang. "Soliton solutions for variable coefficient nonlinear Schr?dinger equation for optical fiber and their application." Acta Physica Sinica 55, no. 8 (2006): 3805. http://dx.doi.org/10.7498/aps.55.3805.

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27

DUAN YI-SHI, YU ZHONG-YUAN, and WU ZHEN-SEN. "SMALL AMPLITUDE SOLITON SOLUTIONS OF THE COUPLED NONLINEAR SCHR?DINGER EQUATIONS IN BIREFRINGENCE OPTICAL FIBER." Acta Physica Sinica 46, no. 12 (1997): 2359. http://dx.doi.org/10.7498/aps.46.2359.

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28

Паасонен, Виктор Иванович, and Михаил Петрович Федорук. "On the efficiency of high-order difference schemes for the Schro¨dinger equation." Вычислительные технологии, no. 6 (December 16, 2021): 68–81. http://dx.doi.org/10.25743/ict.2021.26.6.006.

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Исследуется ряд двух- и трехслойных разностных схем, построенных на расширенных шаблонах, до восьмого порядка точности для уравнения Шрёдингера. Наряду с многоточечными схемами рассматривается метод коррекции Ричардсона в приложении к схеме четвертого порядка аппроксимации, повышающий порядок точности путем построения линейных комбинаций приближенных решений, полученных на различных вложенных сетках. Проведено сравнение методов по устойчивости, сложности реализации алгоритмов и объему вычислений, необходимых для достижения заданной точности. На основе теоретического анализа и численных экспери
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29

宁, 翠. "A Low-Regularity Integrator for the Fourth-Order Nonlinear Schro¨dinger Equation with Almost Mass Conservation." Pure Mathematics 12, no. 10 (2022): 1636–48. http://dx.doi.org/10.12677/pm.2022.1210177.

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30

LIU Yan, 刘燕, and 张素英 ZHANG Su-ying. "Exact Soliton Solution for Quintic-Nonlinear Schrdinger Equation with a Type of Transverse Nonperiodic Modulation." Acta Sinica Quantum Optica 21, no. 2 (2015): 153–59. http://dx.doi.org/10.3788/asqo20152102.0153.

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31

Vysloukh, V. A., A. V. Ivanov, and I. V. Cherednik. "Statistics of the fluctuations of one-soliton solutions of the Schr�dinger equation." Radiophysics and Quantum Electronics 30, no. 8 (1987): 728–37. http://dx.doi.org/10.1007/bf01083483.

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32

CAO QING-JIE, ZHANG TIAN-DE, LI JIU-PING, G.W.PRICE, K.DJIDJELI, and E.H.TWIZELL. "STUDY OF SOLITON SOLUTIONS OF A CLASS OF GENERALIZED NONLINEAR SCHR?DINGER EQUATIONS IN N-SPACE." Acta Physica Sinica 46, no. 11 (1997): 2166. http://dx.doi.org/10.7498/aps.46.2166.

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33

Beibei, Hu, Zhang Ling, Fang Fang, and Zhang Ning. "Riemann-Hilbert approach for a mixed coupled nonlinear Schrödinger equations and its soliton solutions." Journal of University of Science and Technology of China 51, no. 3 (2021): 196–201. http://dx.doi.org/10.52396/just-2021-0059.

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34

DU Zhi-feng, 杜志峰, 宋丽军 SONG Li-jun, and 杨荣草 YANG Rong-cao. "Effect of Group Velocity and Phase Velocity on a Soliton in the Hierarchy of Nonlinear Schrdinger Equation." Acta Sinica Quantum Optica 24, no. 3 (2018): 309–18. http://dx.doi.org/10.3788/jqo20182403.0601.

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35

CHEN, GuanWei, and ShiWang MA. "Non-periodic discrete nonlinear Schr#246;dinger equations with unbounded potentials and general temporal frequencies: In nitely many solitons." SCIENTIA SINICA Mathematica 44, no. 8 (2014): 843–56. http://dx.doi.org/10.1360/012014-37.

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36

Liu, Xuan, Muhammad Ahsan, Masood Ahmad, et al. "Applications of Haar Wavelet-Finite Difference Hybrid Method and Its Convergence for Hyperbolic Nonlinear Schrödinger Equation with Energy and Mass Conversion." Energies 14, no. 23 (2021): 7831. http://dx.doi.org/10.3390/en14237831.

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This article is concerned with the numerical solution of nonlinear hyperbolic Schro¨dinger equations (NHSEs) via an efficient Haar wavelet collocation method (HWCM). The time derivative is approximated in the governing equations by the central difference scheme, while the space derivatives are replaced by finite Haar series, which transform it to full algebraic form. The experimental rate of convergence follows the theoretical statements of convergence and the conservation laws of energy and mass are also presented, which strengthens the proposed method to be convergent and conservative. The H
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37

刘, 学. "Four Types of Functions Solutions of the Novel Auxiliary Equation and Its Application on the Perturbed Nonlinear Schro¨dinger Equation." Advances in Applied Mathematics 04, no. 03 (2015): 217–23. http://dx.doi.org/10.12677/aam.2015.43027.

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38

LIU ZHONG-ZHU and HUANG NIAN-NING. "SOLITON SOLUTIONS OF THE GENERALIZED NONLINEAR SCHR?DINGER EQUATION WITH HIGHER-ORDER CORRECTIONS BY THE DIRECT METHOD OF HIROTA." Acta Physica Sinica 40, no. 1 (1991): 1. http://dx.doi.org/10.7498/aps.40.1.

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39

Zhou, Haoqi, Shuwei Xu, and Maohua Li. "Peregrine Rogue Waves Generated by the Interaction and Degeneration of Soliton-Like Solutions: Derivative Nonlinear Schrödinger Equation." Journal of Applied Mathematics and Physics 08, no. 12 (2020): 2824–35. http://dx.doi.org/10.4236/jamp.2020.812208.

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40

Its, A. R., and A. F. Ustinov. "Formulation of scattering theory for the nonlinear Schr�dinger equation with boundary conditions of the finite density type in a soliton-free sector." Journal of Soviet Mathematics 54, no. 3 (1991): 900–905. http://dx.doi.org/10.1007/bf01101118.

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41

Stephanovich, V. A., W. Olchawa, E. V. Kirichenko, and V. K. Dugaev. "1D solitons in cubic-quintic fractional nonlinear Schrödinger model." Scientific Reports 12, no. 1 (2022). http://dx.doi.org/10.1038/s41598-022-19332-z.

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AbstractWe examine the properties of a soliton solution of the fractional Schrö dinger equation with cubic-quintic nonlinearity. Using analytical (variational) and numerical arguments, we have shown that the substitution of the ordinary Laplacian in the Schrödinger equation by its fractional counterpart with Lévy index $$\alpha$$ α permits to stabilize the soliton texture in the wide range of its parameters (nonlinearity coefficients and $$\alpha$$ α ) values. Our studies of $$\omega (N)$$ ω ( N ) dependence ($$\omega$$ ω is soliton frequency and N its norm) permit to acquire the regions of ex
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42

Mishra, Manoj, Sandeep Kumar Kajala, Mohit Sharma, Swapan Konar, and Soumendu Jana. "Generation, dynamics and bifurcation of high power soliton beams in cubic-quintic nonlocal nonlinear media." Journal of Optics, March 16, 2022. http://dx.doi.org/10.1088/2040-8986/ac5e52.

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Abstract This article presents the generation and propagation dynamics of a high power Gaussian soliton beam through a highly nonlocal nonlinear media having cubic-quintic nonlinearity. Solitons are also generated with lesser explored Hermite super-Gaussian, Hermite cosh-Gaussian and Hermite cosh-super-Gaussian beam profiles. The the governing nonlocal nonlinear Schr\"{o}dinger equation yields matching solitons analytically using variational method as well as numerically using split-step Fourier method. Linear stability analysis identifies the parametric space for stability of the solitons aga
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43

Zhong, Yu, H. Triki, and Qin Zhou. "Analytical and numerical study of chirped optical solitons in a spatially inhomogeneous polynomial law fiber with parity-time symmetry potential." Communications in Theoretical Physics, November 23, 2022. http://dx.doi.org/10.1088/1572-9494/aca51c.

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Abstract This work studies the dynamical transmission of chirped optical solitons in a spatially inhomogeneous nonlinear fiber with cubic-quintic-septic nonlinearity, weak nonlocal nonlinearity, self-frequency shift and parity-time ($\mathcal{PT}$) symmetry potential. A generalized variable-coefficient nonlinear Schr"{o}dinger equation that models the dynamical evolution of solitons has been investigated by the analytical method of similarity transformation and the numerical mixed method of split-step Fourier method and Runge-Kutta method. The analytical self-similar bright and kink solitons,
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44

Bilal, Muhammad, Muhammad Younis, Shafqat-Ur-Rehman, Jamshad Ahmad, and Usman Younas. "Investigation of new solitons and other solutions to the modified nonlinear Schro¨dinger equation in ocean engeneering." Journal of Ocean Engineering and Science, April 2022. http://dx.doi.org/10.1016/j.joes.2022.04.031.

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45

Younas, Usman, T. A. Sulaiman, Jingli Ren, and A. Yusuf. "Investigation of optical solitons and other solutions in optic fibers modelled by the improved perturbed nonlinear Schro¨dinger equation." Journal of Ocean Engineering and Science, June 2022. http://dx.doi.org/10.1016/j.joes.2022.06.038.

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46

Souleymanou, Abbagari, Alphonse Houwe, Lanre Akinyemi, Mustafa Inc, and Bouetou Thomas Bouetou. "Discrete modulation instability and localized modes in chiral molecular chains with first- and third-neighbor interactions." Physica Scripta, January 15, 2023. http://dx.doi.org/10.1088/1402-4896/acb329.

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Abstract In this paper, we examined the behavior of the modulated waves patterns and nonlinear supratransmission phenomenon in gyrotropy molecular chains where the first neighbor and third-neighbor interaction are considered. We have established the propagation modes through the dispersion law showing two cutoff frequencies. Through the numerical simulation we have depicted modulated waves, solitons interaction as well as the modulation instability growth rates brought by the variation of the third-neighbor interaction and effective mass. As it was predicted that the group velocities vanish at
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47

Zhou, Siqi, Jiapeng Liu, Siran Chen, and Yuqin Yao. "The nth-Darboux Transformation and Explicit Solutions of the PT-Symmetry Second-Type Derivative Nonlinear Schrödinger Equation." Journal of Nonlinear Mathematical Physics, March 2, 2022. http://dx.doi.org/10.1007/s44198-022-00045-w.

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AbstractNon-local problems have become one of the research hotspots in recent years since Ablowitz–Musslimani constructed an integrable non-local nonlinear $$\hbox {Schr}\ddot{\mathrm{o}}\hbox {dinger}$$ Schr o ¨ dinger (NLS) equation in 2013. In this paper, we first derive the PT-symmetry second derivative nonlinear $$\hbox {Schr}\ddot{\mathrm{o}}\hbox {dinger}$$ Schr o ¨ dinger (PT-DNLSII) equation. Then we present the nth-Darboux transformation (DT) of the PT-DNLSII equation. As applications, starting from the zero seed solution and non-zero periodic seed solution, the explicit expressions
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48

"Statistical Approach to Nonlinear Schro ̈ dinger Equation. Quantum Case." Applied Mathematics & Information Sciences 16, no. 4 (2022): 617–21. http://dx.doi.org/10.18576/amis/160415.

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49

Tang, Lu. "Bifurcation Analysis and Multiple Solitons in Birefringent Fibers with Coupled Schro¨Dinger-Hirota Equation." SSRN Electronic Journal, 2022. http://dx.doi.org/10.2139/ssrn.4069646.

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50

Chow, K. W. "Logarithmic nonlinear Schro··dinger equation and irrotational, compressible flows: An exact solution." Physical Review E 84, no. 1 (2011). http://dx.doi.org/10.1103/physreve.84.016308.

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