Article
Mathematics
Qianqian Bai, Xiaoguang Li, Li Zhang
Summary: In this study, we investigate the blow-up solutions of coupled nonlinear Schrodinger equations. By considering the conservation of mass and energy, we establish two sufficient conditions for the existence of radially symmetric blow-up solutions. Our results improve upon the previous study by Li and Wu [10], as we no longer assume finite variance.
ACTA MATHEMATICA SCIENTIA
(2023)
Article
Optics
Rongcao Yang, Jing Chen, Xiaoqin Bai, Heping Jia, Juan Bai
Summary: In this study, a coupled nonlocal nonlinear Schrodinger equation with self-induced parity-time (PT) symmetric potential is considered, and diverse evolution patterns of amplitude-phase modulated composite waves are investigated. It is found that the coupled nonlocal model can be decoupled into nNLSEs with self-induced PT symmetric potential under certain constraints through a general linear transformation with amplitude and phase modulation. Various composite waves composed of bright and/or dark soliton solutions, rogue waves, bright/dark solitons, and periodic solitons are studied based on the exact solutions of the nNLSEs with self-induced PT potential, and abundant evolution patterns under amplitude-phase modulation are presented. The results only demonstrate the characteristics of limited superposed composite waves. In fact, there exist infinite possible evolution patterns of composite waves due to the arbitrary amplitude-phase modulation in the coupled nonlocal nonlinear system with self-induced PT symmetric potential.
Article
Mathematics, Applied
Eduardo Colorado, Alejandro Ortega
Summary: In this work, we study a class of systems of coupled nonlinear fractional Schrodinger equations and prove the existence of positive radial bound and ground state solutions under appropriate parameter conditions.
ADVANCES IN DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Wen-Bo Bo, Ru-Ru Wang, Wei Liu, Yue-Yue Wang
Summary: The symmetry breaking of solitons in the nonlinear Schrodinger equation with cubic-quintic competing nonlinearity and parity-time symmetric potential is studied. It is found that symmetric fundamental solitons and symmetric tripole solitons tend to be stable, while asymmetric solitons are unstable in both high and low power regions. Increasing saturable nonlinearity widens the stability region of fundamental symmetric solitons and symmetric tripole solitons.
Article
Multidisciplinary Sciences
Dongdong Sun
Summary: In this paper, we investigate the uniqueness and symmetry of solutions to nonlinear Schrodinger-Kirchhoff equations with constant coefficients, demonstrate the uniqueness of solutions to nonlinear Schrodinger-Kirchhoff equations with polynomial potential, and analyze the asymptotic behavior of positive least energy solutions to nonlinear Schrodinger-Kirchhoff equations with vanishing potentials.
Article
Mathematics, Applied
Zijian Zhou, Jin Song, Weifang Weng, Zhenya Yan
Summary: This paper examines the properties of two types of PT-symmetric non-periodic potentials in the logarithmic nonlinear Schrodinger equation, including the existence, stability, and interaction of solitons, as well as the impact of time-dependent functions on solitons.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Zhouji Ma, Xiaojun Chang
Summary: This paper investigates the nonlinear biharmonic Schrödinger equation with combined power-type nonlinearities in R-N space. By analyzing the behavior of the ground state energy with respect to the prescribed mass, the existence of normalized ground state solutions is established. Furthermore, it is proven that all ground states are local minima of the associated energy functional.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Physics, Fluids & Plasmas
Yinong Tai, Hongwei Li, Zhaojie Zhou, Ziwen Jiang
Summary: In this paper, the numerical solution of coupled nonlinear Klein-Gordon equations on unbounded domains is solved using the artificial boundary method. By introducing artificial boundaries and designing local artificial boundary conditions, the original problem is transformed into an initial boundary value problem on a bounded domain, which can be efficiently solved using the finite difference method. Numerical examples are provided to validate the proposed method's accuracy and effectiveness.
Article
Mathematics
Kazuyuki Yagasaki, Shotaro Yamazoe
Summary: This article studies bifurcations and spectral stability of solitary waves in coupled nonlinear Schrodinger (CNLS) equations on the line. Under the assumption that the coupled equations possess a solution in which one component is identically zero, called a fundamental solitary wave, the authors establish criteria for the pitchfork bifurcation of the fundamental solitary wave. The authors utilize the Hamiltonian-Krein index theory and Evans function technique to determine the spectral and/or orbital stability of the bifurcated solitary waves and the fundamental one under nondegenerate conditions that are easy to verify compared to previous results. The theory is applied to a cubic nonlinearity case, and numerical evidence is provided for the theoretical results.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Chang-En Du, Ching-Sung Liu
Summary: In this paper, a Newton-Noda iteration (NNI) method is proposed to find the ground state of nonlinear Schrodinger equations. Numerical experiments are performed to validate the performance of the method.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Olivier Goubet, Ezzeddine Zahrouni
Summary: In this paper, we investigate the existence of a global attractor for a damped forced nonlinear logarithmic Schrodinger equation in R-N. We also discuss some open issues for nonlinear logarithmic Schrodinger equations within the framework of infinite-dimensional dynamical systems.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2021)
Article
Mathematics, Applied
Haifeng Wang, Yufeng Zhang
Summary: In this paper, a new integrable coupling system of the focusing nonlinear Schrodinger equation, called the extended coupled nonlinear Schrodinger (ECNLS) equations, is introduced based on the non-semisimple Lie algebra. The asymptotic behavior, analyticity, and symmetry of the eigenfunctions and scattering coefficients are analyzed based on a 4th-order block matrix spectral problem. Solutions are formulated for the Riemann-Hilbert problems associated with the reflectionless transforms, and N-soliton solutions of the ECNLS equations are generated. Furthermore, the ECNLS equations are extended to a multi-component nonlinear Schrodinger system, allowing for an arbitrary number of components and the possibility of describing new nonlinear phenomena.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Engineering, Mechanical
Yu-Shan Bai, Ya-Na Liu, Wen-Xiu Ma
Summary: In this paper, the properties of the multi-component nonlinear Schrodinger equations (MNLS) are investigated using the Lie symmetry method. The symmetries and reductions of the equations are derived, and some explicit solutions as well as conservation laws are constructed.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Yanyun Wen, Peihao Zhao
Summary: This paper studies the solutions of the nonlinear Maxwell equations under certain conditions and proves the existence of infinitely many cylindrical symmetry solutions that satisfy the conditions.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Mathematics, Applied
Xueqin Peng, Gao Jia, Chen Huang
Summary: This paper considers the existence and asymptotic behavior of solutions to a quasilinear Schrödinger-Poisson system with exponential and logarithmic nonlinearities, proving the existence of at least one nonnegative pair of solutions and improving some existing results. The novelty of the system lies in the intersection among the quasilinear, logarithmic, and exponential critical terms.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mechanics
Konstantin G. Zloshchastiev
JOURNAL OF THEORETICAL AND APPLIED MECHANICS
(2019)
Article
Physics, Nuclear
Konstantin G. Zloshchastiev
INTERNATIONAL JOURNAL OF MODERN PHYSICS A
(2020)
Article
Physics, Applied
Tony C. Scott, Konstantin G. Zloshchastiev
LOW TEMPERATURE PHYSICS
(2019)
Article
Astronomy & Astrophysics
Konstantin G. Zloshchastiev
Article
Astronomy & Astrophysics
Konstantin G. Zloshchastiev
Article
Physics, Applied
Konstantin G. Zloshchastiev
Summary: Within the theory of strongly-interacting quantum Bose liquids, a general relativistic model of self-interacting complex scalar fields with logarithmic nonlinearity is considered, demonstrating the existence of gravitational equilibria described by spherically symmeric nonsingular finite-mass asymptotically-flat solutions. These equilibrium configurations can describe massive astronomical objects like bosonized superfluid stars or neutron star cores, as well as finite-size particles and non-topological solitons like Q-balls, with estimates for their masses and sizes provided.
LOW TEMPERATURE PHYSICS
(2021)
Article
Physics, Applied
Konstantin G. Zloshchastiev
Summary: The study investigates the dynamical properties of density fluctuations in cigar-shaped Bose-Einstein condensates in different traps, showcasing that density fluctuations in strongly anisotropic traps are essentially one-dimensional and exhibit different forms of oscillations based on the sign of nonlinear coupling. Additionally, the behavior of linear particle density and energy varies depending on the value of the nonlinear coupling, affecting the growth patterns of density and energy in the system.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2021)
Article
Astronomy & Astrophysics
Ekaterina Belendryasova, Vakhid A. Gani, Konstantin G. Zloshchastiev
Summary: This study investigates a (1 + 1)-dimensional Lorentz-symmetric field-theoretic model with a logarithmic potential and Mexican-hat form, allowing for topological solutions - kinks. The analysis shows that the kink excitation spectrum in this model does not contain vibrational modes, and differentiates two regimes in kink-antikink collisions.
Article
Physics, Fluids & Plasmas
Konstantin G. G. Zloshchastiev
Summary: A comparative study is conducted to analyze the propagation of sound pulses in elongated Bose liquids and Bose-Einstein condensates using the Gross-Pitaevskii and logarithmic models. The study shows that the propagation of small density fluctuations is essentially one-dimensional in both models. It also reveals that the speed of sound scales differently in the two cases, with a square root dependence on particle density in the Gross-Pitaevskii liquid/condensate case and a constant value in the homogeneous logarithmic liquid case.
Article
Physics, Multidisciplinary
Konstantin G. Zloshchastiev
Summary: The logarithmic superfluid theory proposes a multi-scale structure of gravity, and by applying best-fitting procedures to rotation curve data, the theory's predictions on galactic scale are found to closely correspond with observational data.
PRAMANA-JOURNAL OF PHYSICS
(2022)
Article
Physics, Multidisciplinary
M. Kraiev, K. Domina, V Kraieva, K. G. Zloshchastiev
Summary: The theory explains density inhomogeneities in materials undergoing liquid-solid phase transitions through solitonic solutions of logarithmic wave equations, such as bubbles or cells. Experimental evidence shows periodicity in the polycrystalline structure of metal grains and Gaussian-like profiles of microhardness within grains.
INDIAN JOURNAL OF PHYSICS
(2022)
Proceedings Paper
Physics, Multidisciplinary
Konstantin G. Zloshchastiev
INTERNATIONAL CONFERENCE PHYSICA.SPB/2019
(2019)
Proceedings Paper
Mathematics, Applied
M. Kraiev, K. Domina, V. Kraieva, K. G. Zloshchastiev
XXVI INTERNATIONAL CONFERENCE ON INTEGRABLE SYSTEMS AND QUANTUM SYMMETRIES
(2019)
Proceedings Paper
Quantum Science & Technology
Ludmila Praxmeyer, Konstantin G. Zloshchastiev
32ND INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN PHYSICS (GROUP32)
(2019)
Proceedings Paper
Astronomy & Astrophysics
E. Belendryasova, V. A. Gani, K. G. Zloshchastiev
4TH INTERNATIONAL CONFERENCE ON PARTICLE PHYSICS AND ASTROPHYSICS (ICPPA-2018)
(2019)