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Article
Mathematics, Applied
Xin-Yi Gao et al.
Summary: Investigations on electromagnetic-wave/ferromagnetic-material interactions in magneto-optic recording and computer data storage have been conducted. A variable-coefficient modified Kadomtsev-Petviashvili system for certain electromagnetic waves in an isotropic charge-free infinite ferromagnetic thin film was studied, with potential applications in magneto-optic recording. Symbolic computation was used to derive auto-Backlund transformations, bilinear forms, and N-solitonic solutions with varying coefficients for electromagnetic waves in ferromagnetic films.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Interdisciplinary Applications
Kang-Jia Wang et al.
Summary: This study proposes the fractal regularized long-wave equation for describing shallow water waves under unsmooth boundaries. The solitary wave solution is obtained using the fractal variational method, and it is found that the fractal order can affect the wave morphology, but not its peak value.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Interdisciplinary Applications
Kang-Jia Wang
Summary: This paper investigates the nonlinear vibration of carbon nanotubes embedded in a fractal medium. The fractal variational principle is established and proven to have a strong minimum condition. The Hamiltonian theory combined with the residual equation is used to find the solution of the fractal nonlinear vibration. The impacts of different fractal orders on the vibration characteristics are also presented.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Engineering, Multidisciplinary
Wen-Xiu Ma
Summary: This paper analyzes N-soliton solutions and explores the Hirota N-soliton conditions for scalar (1 + 1)-dimensional equations within the Hirota bilinear formulation. An algorithm is proposed to verify the Hirota conditions by factoring out common factors in N wave vectors of the Hirota function and comparing degrees of involved polynomials. Applications to a class of generalized KdV equations and a class of generalized higher-order KdV equations are made, with proofs of the existence of N-soliton solutions provided for all equations in the two classes.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2022)
Article
Optics
Kang-Jia Wang
Summary: The current work considers the Fokas system for nonlinear pulse propagation in monomode optical fibers. By using the Exp-function method, six families of exact soliton solutions were successfully constructed, and their behaviors were described through 3-D contours. The results indicate that the Exp-function method is effective in constructing abundant exact solutions for partial differential equations in optics.
Article
Mathematics, Applied
Wen-Xiu Ma
Summary: This study proposes a nonlocal real reverse-spacetime integrable hierarchies of PT symmetric matrix AKNS equations, achieved through nonlocal symmetry reductions on the potential matrix, to determine generalized Jost solutions. By applying the Sokhotski-Plemelj formula, the associated Riemann-Hilbert problems are transformed into integral equations of Gelfand-Levitan-Marchenko type. The Riemann-Hilbert problems corresponding to the reflectionless case are explicitly solved, presenting soliton solutions for the resulting nonlocal real reverse-spacetime integrable PT-symmetric matrix AKNS equations.
PHYSICA D-NONLINEAR PHENOMENA
(2022)
Article
Mathematics, Applied
Meng Wang et al.
Summary: This study investigates the ultrashort optical pulses in a birefringent optical fiber through solving a coupled fourth-order nonlinear Schrödinger system. Soliton interactions, polarizations changes with beta value variations, and other nonlinear effects are analyzed and graphically displayed in the research.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Interdisciplinary Applications
Kang-Le Wang
Summary: In this study, a new fractal derivative is used to describe a nonlinear oscillator model, and a variational principle of the fractal model is successfully established using the fractal semi-inverse transform method to obtain an approximate frequency. Numerical results demonstrate that the proposed technique is simple and accurate for fractal nonlinear oscillators.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Mathematics, Applied
Xin-Yi Gao et al.
Summary: Recent progress in optical fibers has led to various applications in fields such as nonlinear Schrodinger-type models and symbolic computation. A study on a three-coupled variable-coefficient nonlinear Schrodinger system has provided valuable insights and analytical solutions for picosecond-pulse attenuation/amplification in multicomponent inhomogeneous optical fibers.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Interdisciplinary Applications
Dan-Yu Yang et al.
Summary: This paper investigates a variable-coefficient coupled Hirota system describing vector optical pulses in an inhomogeneous optical fiber. By constructing a Lax pair and a Darboux transformation, bright-bright soliton, bright-dark soliton, and breather solutions are obtained. Interactions between solitons and the decrease in period of bright-dark solitons under certain conditions are highlighted in the study.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Computer Science, Interdisciplinary Applications
Wen-Xiu Ma
Summary: This study focuses on constructing N-soliton solutions within the Hirota bilinear formulation and analyzing the Hirota N-soliton conditions in (2+1)-dimensions. A generalized algorithm for proving the Hirota conditions is presented, along with the introduction of two weight numbers to achieve homogeneity of the related polynomials. An application is developed for a general combined nonlinear equation to provide proof of existence of its N-soliton solutions.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Mathematics, Interdisciplinary Applications
Kang-jia Wang et al.
Summary: This study proposes a modified equal width equation with fractal derivatives to study the motion morphology of ion-acoustic waves in plasma. By utilizing the fractal variational formulation and He's variational method, combined with a two-scale transform, the periodic and solitary wave solutions of the equation are successfully found, opening up new perspectives for the study of traveling wave theory in fractal space.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Optics
Kang-Jia Wang
Summary: This study applied an ancient Chinese algorithm called Ying Bu Zu Shu to find periodic solution of the time-space fractional modified form of the complex nonlinear Fokas-Lenells equation, proving the effectiveness and reliability of the proposed method. By plotting the solutions with different fractional orders in 2-dimensional and 3-dimensional surfaces, it provides valuable insights for the study of periodic solutions in physics.
Article
Mathematics, Applied
Wen-Xiu Ma
Summary: In this study, a combined pKP-BKP equation is introduced by considering a linear combination of the potential KP equation and the BKP equation. It is proven that the combined pKP-BKP equation satisfies the Hirota N-soliton condition and possesses an N-soliton solution. The proof involves comparing degrees of homogeneous polynomials associated with the Hirota function in N wave vectors.
JOURNAL OF GEOMETRY AND PHYSICS
(2021)
Article
Mathematics, Applied
Yuan Shen et al.
Summary: Researchers investigated water waves and proposed a nonlinear evolution equation, along with soliton solutions. The results depend on the water-wave coefficients in the equation.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Materials Science, Multidisciplinary
Kang-Jia Wang
Summary: The paper focuses on the coupled Konno-Oono equation in the magnetic field, obtaining 15 sets of analytical solutions using three effective technologies: simplified extended tanh-function method, variational direct method, and He's frequency formulation. The behavior of the solutions is plotted through 3-D contours, demonstrating the effectiveness and power of the proposed methods for the study of traveling wave theory in physics.
RESULTS IN PHYSICS
(2021)
Article
Physics, Multidisciplinary
Muhammad Sohail et al.
Summary: This report investigates the flow of non-Newtonian fluids down a bilateral surface under the influence of a magneto-hydrodynamic effect. It examines the movement of particles generated by the movement of walls in horizontal and vertical directions. The study includes thermal analysis and modeling of energy transport and species conservation.
Article
Mathematics, Interdisciplinary Applications
Xin-Yi Gao et al.
Summary: In this study, we focused on shallow water waves near an ocean beach or in a lake, and discovered two hetero-Backlund transformations and a set of similarity reductions through the Bell polynomials and symbolic computation. These findings provide solutions to a known ordinary differential equation, based on the dispersive power of oceanic water waves, aiming to assist researchers in exploring certain modes of shallow water waves.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Kang-Jia Wang et al.
Summary: In this study, we aim to find the explicit solutions of the Benney-Luke equation using a novel approach called the variational direct method (VDM). The VDM, based on variational theory and Ritz-like method, simplifies the equation and obtains optimal solutions through stationary conditions. The results, presented in 3-D plots, 2-D curves, and 2-D contours, show that VDM is simple, intuitive, and powerful, potentially opening new perspectives for traveling wave theory.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Acoustics
Wen-Xiu Ma et al.
Summary: In this study, soliton solutions for the B-type Kadomtsev-Petviashvili equation are analyzed and the Hirota N-soliton condition is verified within the Hirota bilinear formulation. A weight number is used in an algorithm to check the Hirota condition while transforming the Hirota function in N wave vectors to a homogeneous polynomial. Soliton solutions are presented under general dispersion relations.
Article
Materials Science, Multidisciplinary
Kang-Jia Wang et al.
Summary: In this paper, a novel and simple approach called the variational direct method (VDM) is applied to construct the exact traveling wave solutions of the system of ion sound and Langmuir waves. The obtained results show that the VDM is simple, straightforward, and powerful, which is expected to open new perspectives for the traveling wave theory.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Applied
Raghda A. M. Attia et al.
Summary: This research explores the DNA model using various methods to obtain analytical, semi-analytical, and numerical solutions, revealing the dynamic characteristics within the DNA molecule and the correlations between different solutions. The validation and stability checks of these solutions provide powerful tools for investigating nonlinear equations.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2021)
Article
Physics, Multidisciplinary
K. K. Ali et al.
Summary: This study examines the Gilson-Pickering equation using the sine-Gordon expansion method, successfully constructing various exact solitary wave solutions and analyzing the stability. The 2D, 3D, and contour surfaces for all solutions are also plotted.
INDIAN JOURNAL OF PHYSICS
(2021)
Article
Engineering, Mechanical
Li Bang-Qing et al.
NONLINEAR DYNAMICS
(2020)
Article
Materials Science, Multidisciplinary
Aniqa Zulfiqar et al.
RESULTS IN PHYSICS
(2020)
Article
Engineering, Electrical & Electronic
Wen-Xiu Ma
OPTICAL AND QUANTUM ELECTRONICS
(2020)
Article
Physics, Multidisciplinary
Kang-Jia Wang
EUROPEAN PHYSICAL JOURNAL PLUS
(2020)
Article
Multidisciplinary Sciences
F. M. Allehiany et al.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE
(2020)
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Mukesh Kumar et al.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2019)
Article
Physics, Multidisciplinary
Behzad Ghanbari et al.
FRONTIERS IN PHYSICS
(2019)
Article
Optics
Qin Zhou et al.
JOURNAL OF MODERN OPTICS
(2016)
Article
Physics, Multidisciplinary
D. Daghan et al.
BRAZILIAN JOURNAL OF PHYSICS
(2016)
Article
Engineering, Multidisciplinary
Anjan Biswas et al.
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
(2012)
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Engineering, Mechanical
E. V. Krishnan et al.
NONLINEAR DYNAMICS
(2011)
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Mathematics, Interdisciplinary Applications
Xu-Hong (Benn) Wu et al.
CHAOS SOLITONS & FRACTALS
(2008)
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Mathematics, Applied
Abdul-Majid Wazwaz
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2007)
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Mathematics, Applied
Xu-Hong (Benn) Wu et al.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2007)
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Mathematics, Interdisciplinary Applications
Ji-Huan He et al.
CHAOS SOLITONS & FRACTALS
(2006)
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Mathematics, Interdisciplinary Applications
ZT Fu et al.
CHAOS SOLITONS & FRACTALS
(2004)
