Article
Materials Science, Multidisciplinary
Qin Zhou, Yunzhou Sun, Houria Triki, Yu Zhong, Zhongliang Zeng, Mohammad Mirzazadeh
Summary: This paper investigates the propagation properties of optical soliton pulses with higher-order effects in a multimode fiber and proposes a method to control the physical properties of solitons by choosing different parameters.
RESULTS IN PHYSICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Cui-Cui Ding, Qin Zhou, Si-Liu Xu, Yun-Zhou Sun, Wen-Jun Liu, Dumitru Mihalache, Boris A. Malomed
Summary: In this study, we investigate the controlled evolution of nonautonomous solitons in a spinor Bose-Einstein condensate. By analyzing a system of three coupled Gross-Pitaevskii equations with spatiotemporal modulation, we derive an integrability condition and a nonisospectral Lax pair. This allows us to obtain an infinite set of dynamical invariants and generate one- and two-soliton solutions using the Darboux transform. We find various solutions for controlled nonautonomous solitons, including self-compressed, snake-like, stepwise solitons, and even rogue wave-like states.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Multidisciplinary
Atanas Stefanov, Georgios A. Tsolias, Jesus Cuevas-Maraver, Panayotis G. Kevrekidis
Summary: This paper provides a characterization of the ground states of a higher-dimensional quadratic-quartic model and investigates the stability of the system under different parameters. It is found that the stability of the system is influenced within a certain parameter range, and there exists a range of stable frequencies.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Optics
T. L. Belyaeva, M. A. Aguero, V. N. Serkin
Summary: The introduced nonautonomous solitons in the nonautonomous nonlinear Schrodinger equation model can interact elastically under different external potentials and are only controlled under certain conditions; novel features arise due to the dependence between soliton amplitudes and velocities, such as the decay of soliton bound states.
Article
Optics
Sudipta Nandy, Gautam K. Saharia, Sagardeep Talukdar, Riki Dutta, Rahul Mahanta
Summary: This study investigates the hierarchies of nonautonomous Nonlinear Schrodinger equation (NLSE), presenting soliton solutions and reversible transformations. Crucial differences between even and odd order hierarchies are analyzed, with constraints identified among dispersion and nonlinear coefficients. The findings offer a universal mathematical platform for studying diverse physical systems.
Article
Optics
M. S. Mani Rajan, S. Saravana Veni
Summary: We studied the behavior of three nonautonomous solitons in an optical fiber with inhomogeneous nature using the nonlinear Schrödinger equation with nonautonomous term. By constructing matrices with the AKNS procedure, we obtained three soliton solutions and demonstrated their switchable characteristics through graphical illustrations. These findings have important implications for the design of optical logic gate devices in optical computing.
Article
Physics, Multidisciplinary
Wen-Xuan Hao, Yan Wang, Lu Li
Summary: In this paper, a generalized nonlinear Schrodinger equation with various dispersions, nonlinearity, and gain/loss is investigated. Exact self-similar soliton solutions are constructed, and the corresponding propagation dynamics in a periodically modulated fiber system are studied. Results show periodic oscillatory evolution behavior of soliton solutions in the absence of gain/loss, and the implementation of a dark soliton switch with periodic modulation of gain/loss. Stability of self-similar solutions against constraint deviations and initial perturbations is also investigated through direct numerical simulations.
ROMANIAN REPORTS IN PHYSICS
(2021)
Article
Physics, Multidisciplinary
Dan-Yu Yang, Bo Tian, Cong-Cong Hu, Tian-Yu Zhou
Summary: Optical communication systems are important for modern long-distance communication networks due to their low-loss transmission and high capacity. In this study, we investigate the optical nonlinear waves in a birefringent fiber using a coupled nonlinear Schrodinger system with four-wave mixing terms. We construct a generalized Darboux transformation and obtain higher-order rogue-wave solutions. Based on these solutions, we present various structures of second-order and third-order rogue waves.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Materials Science, Multidisciplinary
Mengyao Guo, Xiyang Xie
Summary: This paper presents two- and three-soliton solutions for a higher-order matrix nonlinear Schrodinger equation using the binary Darboux transform. The interaction properties of the solitons are analyzed, revealing various types of interactions such as breather-like solitons, bound-state solitons, and solitons with different peak structures. The interactions of three solitons are also investigated, resulting in seven interesting appearances including shape-changing and shape-preserving interactions.
RESULTS IN PHYSICS
(2023)
Article
Physics, Multidisciplinary
Yue-Jin Cai, Jian-Wen Wu, Lang-Tao Hu, Ji Lin
Summary: This paper investigates femtosecond nondegenerate solitons in optical fibers, described by coupled higher-order nonlinear Schrodinger equations. Analytical solutions for nondegenerate solitons are constructed using the Hirota method, with constraints for stable structures. In addition, soliton molecules and asymmetric solitons are identified as new types of nondegenerate solitons, with their interactions during propagation studied.
Article
Computer Science, Interdisciplinary Applications
Yu Lou, Yi Zhang
Summary: In this study, a generalized nonlinear Schrodinger equation with higher-order terms is investigated as a model for the nonlinear spin excitations in the one-dimensional isotropic biquadratic Heisenberg ferromagnetic spin. The Darboux transformation of the equation is presented using Riccati equations associated with the Lax pair. By considering complicated Jacobi elliptic functions as seed solutions, breathers in the presence of two kinds of Jacobian elliptic functions are constructed. The dynamical properties of these solutions are analyzed using three-dimensional figures.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Engineering, Mechanical
T. L. Belyaeva, V. N. Serkin
Summary: In this work, we investigate the representation of external potentials in completely integrable higher-order nonautonomous nonlinear dynamical systems as an infinite power series with time-varying coefficients. The study introduces the generalized Hirota equation as an example, demonstrating the elastic interaction of accelerating and self-compressing nonautonomous solitons in various external potentials, based on conditions of exact integrability.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Su -Su Chen, Bo Tian, Qi-Xing Qu, He Li, Yan Sun, Xia-Xia Du
Summary: This paper investigates the propagation of nonlinear Alfven waves in inhomogeneous plasma through a variable-coefficient derivative nonlinear Schrodinger equation. Various properties of Alfven soliton solutions are derived, including width, amplitude, velocity, trajectory, interactions, and collapses. The study provides insights into the behavior of Alfven waves in plasma environments.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Physics, Multidisciplinary
Shubin Wang, Xin Zhang, Guoli Ma, Daiyin Zhu
Summary: In this paper, the bilinear method is used to analyze the coupled high-order nonlinear Schrodinger equations and obtain their three-soliton solutions. The influence of the relevant parameters in the three-soliton solution on the soliton inelastic interaction is studied. The results have potential applications in soliton control, all-optical switching, and optical computing.
Article
Optics
T. L. Belyaeva, A. Mena-Contla, L. Morales-Lara, R. Pena-Moreno, V. N. Serkin
Summary: This research clarifies an analytical approach in the theory of modulational instability within the framework of the nonautonomous nonlinear Schrodinger equation. It reveals important analogies and distinctions between the higher-order induced modulational instability and the internal dynamics of higher-order N-soliton bound states. The study also demonstrates the crucial role of the sliding pump effect in the nonlinear stage of the higher-order induced modulational instability, leading to the soliton self-cleaning effect.
Article
Optics
T. L. Belyaeva, M. A. Aguero, M. E. Maguina-Palma, V. N. Serkin
Summary: This study demonstrates the possibility of generalizing the Karpman and Solov'ev theory of interaction forces among solitons with an external potential as a small perturbation. By closely following the adiabatic perturbation algorithm proposed by Karpman and Solov'ev, analytical solutions are obtained to describe the dynamics of two solitons trapped in a harmonic oscillator potential. The research shows that the oscillation period of in-phase solitons decreases with increasing oscillator frequency and decreasing initial separation, while out-of-phase solitons can exist in states where they practically do not interact.
Article
Physics, Nuclear
Alla Demyanova, Viktar Starastsin, Alexey Ogloblin, Andrey Danilov, Sergey Dmitriev, Wladyslaw Trzaska, Pauli Heikkinen, Tatyana Belyaeva, Sergey Goncharov, Vladimir Maslov, Yuri Sobolev, Yury Gurov, Boris Chernyshev, Nassurlla Burtebaev, Daniyar Janseitov, Sergey Khlebnikov
Summary: A study of the B-11(He-3,d)C-12 reaction at a He-3 energy of 25 MeV was conducted at the University of Jyvaskyla in Finland. Differential cross sections were measured for different states in C-12 with excitation energies around 13.35 MeV and 20 MeV, and analyzed using the DWBA method. Tentative assignments for various states were given, with spin-parity and isospin values determined for the first time.
EUROPEAN PHYSICAL JOURNAL A
(2021)
Article
Engineering, Mechanical
T. L. Belyaeva, V. N. Serkin
Summary: In this work, we investigate the representation of external potentials in completely integrable higher-order nonautonomous nonlinear dynamical systems as an infinite power series with time-varying coefficients. The study introduces the generalized Hirota equation as an example, demonstrating the elastic interaction of accelerating and self-compressing nonautonomous solitons in various external potentials, based on conditions of exact integrability.
NONLINEAR DYNAMICS
(2022)
Article
Optics
T. L. Belyaeva, A. Mena-Contla, L. Morales-Lara, R. Pena-Moreno, V. N. Serkin
Summary: This research clarifies an analytical approach in the theory of modulational instability within the framework of the nonautonomous nonlinear Schrodinger equation. It reveals important analogies and distinctions between the higher-order induced modulational instability and the internal dynamics of higher-order N-soliton bound states. The study also demonstrates the crucial role of the sliding pump effect in the nonlinear stage of the higher-order induced modulational instability, leading to the soliton self-cleaning effect.
Article
Optics
T. L. Belyaeva, M. A. Aguero, V. N. Serkin
Summary: The introduced nonautonomous solitons in the nonautonomous nonlinear Schrodinger equation model can interact elastically under different external potentials and are only controlled under certain conditions; novel features arise due to the dependence between soliton amplitudes and velocities, such as the decay of soliton bound states.
Article
Optics
T. L. Belyaeva, V. N. Serkin
Summary: The study presents the generalized nonautonomous complex modified KdV equation with external potentials, where the conditions for the existence of solitons require the external potentials to satisfy the exact integrability conditions along with nonlinear and dispersive terms.
Article
Optics
M. A. Aguero, T. L. Belyaeva, M. Perez-Maldonado, L. Morales-Lara, R. Pena-Moreno, V. N. Serkin
Summary: The main objective of our study is to reveal the role of cubic-quintic nonlinearity in the dynamics of induced modulational instability in nonautonomous nonlinear optical systems with dispersion and nonlinearity varying along the propagation distance. Analytical methods are used to obtain the criterion of modulational instability in the cubic-quintic nonautonomous systems. The nonlinear stage of modulational instability is studied through direct computational modeling. The main results of our computer experiments clearly demonstrate imperfect spectral energy restoration, leading to variations in the Fermi-Pasta-Ulam recurrence periods, and emphasize the significance of compensating both the quintic nonlinearity and changing dispersion to suppress the appearance of rogue waves.
Article
Optics
M. A. Aguero, T. L. Belyaeva, G. Corro, R. Pena-Moreno, V. N. Serkin
Summary: The objective of this study is to reveal unexpected features of induced modulation instability during its nonlinear stage. The nonlinear stage is investigated through direct computer simulation. The results demonstrate the significant effect of rogue-wave peak power saturation in the zero-gain spectral region. The peak values and subsequent splitting of rogue waves are determined by the total energy stored in one period of an externally modulated quasi-continuous pump wave. The significance of these results lies in the possibility of controlling the formation of rogue waves induced by periodic modulation of the pump.
