Related references
Note: Only part of the references are listed.
Article
Engineering, Mechanical
Lanre Akinyemi et al.
Summary: This paper focuses on studying various solutions and their applications in nonlinear wave models for the extended Kadomtsev-Petviashvili equation. The integrability of the equation is validated using Painleve analysis and WTC-Kruskal algorithm. Different types of solutions are determined using various ansatz's functions and symbolic computation. Visualization of the solutions is performed by selecting appropriate parametric values and utilizing Mathematica 13.1.
NONLINEAR DYNAMICS
(2023)
Article
Materials Science, Multidisciplinary
Yun-Hui Zhao et al.
Summary: This paper investigates the analytical solutions of the autocatalytic reaction-diffusion Selkov-Schnakenberg system from a mathematical perspective. New families of exact solutions are derived using the phi(6)-model expansion technique, representing the autocatalyst and reactant concentrations. The existence of these solutions is discussed under different constraint conditions and in hyperbolic, trigonometric, and rational forms. These results are novel and effective in understanding the physical phenomena of autocatalytic chemical reactions.
RESULTS IN PHYSICS
(2023)
Article
Engineering, Mechanical
Yi-Wei Zhao et al.
Summary: The extended coupled (2+1)-dimensional Burgers system is utilized to describe wave processes in oceanography, acoustics, or hydrodynamics. By employing the Riccati projective equation method and symbolic computation, a variable separation solution is derived. The study focuses on fractal and chaotic structures based on the gradient function (U), and analyzes some excitation properties of the solutions with accompanying figures showing the shape and structure.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Mechanical
Yu-Hang Yin et al.
Summary: The paper investigates a (3+1)-dimensional nonlinear evolution equation to study features and properties of nonlinear dynamics in higher dimensions. By using the Hirota bilinear method, a bilinear Backlund transformation with six free parameters is constructed, resulting in multiple sets of solutions and new types of interaction solutions. The periodic interaction phenomenon is simulated by setting constraints to the new interaction solution expressed by polynomial-cos-cosh test function.
NONLINEAR DYNAMICS
(2022)
Article
Physics, Multidisciplinary
Sayed Saifullah et al.
Summary: In this manuscript, the interaction between lump and kink-soliton solutions for the generalized perturbed KdV equation is extracted using the Hirota bilinear method and Cole-Hopf transformation. The correct value of R is computed, leading to clearer outcomes for various soliton solutions. These solutions are displayed in 2D and 3D space using Mathematica by selecting appropriate parameter values.
Article
Materials Science, Multidisciplinary
Shao-Wen Yao et al.
Summary: The modified auxiliary equation (MAE) approach and the generalized projective Riccati equation (GPRE) method are used for the first time to solve the Zoomeron problem and obtain various types of exact traveling wave solutions. The governing model covers unique examples of solitons with distinct properties in different physical situations. The obtained results are given in the form of hyperbolic and trigonometric functions, and the dynamical features are demonstrated through interesting plots.
RESULTS IN PHYSICS
(2022)
Article
Physics, Applied
Bing Liu et al.
Summary: Based on the coupled nonlinear volatility and option pricing model, this study introduces a new external potential on the option price to a coupled nonlinear Schrodinger model. Numerical solutions and rogue wave solutions are derived to explore the influence of external potential on option price fluctuation and financial rogue waves.
MODERN PHYSICS LETTERS B
(2022)
Article
Physics, Multidisciplinary
Souleymanou Abbagari et al.
Summary: This paper investigates the behavior of modulated waves and W-shaped profiles in birefringent fibers with anti-cubic nonlinear terms. Through numerical and analytical methods, it is found that the anti-cubic nonlinear terms and cross-phase modulation can increase the growth rate and amplitude of modulation instability.
Article
Materials Science, Multidisciplinary
Aasma Khalid et al.
Summary: This article presents an innovative strategy using cubic splines to solve 14th-order nonlinear boundary value problems. By transforming the problems into a system of linear equations and utilizing both cubic polynomial spline and cubic non-polynomial spline, accurate solutions and derivative estimates are obtained.
RESULTS IN PHYSICS
(2022)
Article
Engineering, Marine
Daniel Ntiamoah et al.
Journal of Ocean Engineering and Science
(2022)
Article
Mathematics, Interdisciplinary Applications
K. Hosseini et al.
Summary: The main goal of this paper is to analyze the impact of the Coriolis parameter on nonlinear waves by studying the geophysical KdV equation. Specific transformations are used to derive the one-dimensional and operator forms of the equation. Solitons and complexitons are retrieved using well-established approaches, and a new conservation theorem is employed to extract conservation laws. The results show that, within certain parameter regimes, increasing the Coriolis parameter speeds up the convergence of the free surface elevation to zero.
GEM-INTERNATIONAL JOURNAL ON GEOMATHEMATICS
(2022)
Article
Physics, Multidisciplinary
Muhammad Naveed Rafiq et al.
Summary: This work utilizes the unified method and beta derivative to find new and interesting traveling wave solutions for the space-time fractional modified equal width equation. The obtained results are consistent with polynomial and rational forms of nonlinear evolution equations and meet the requirements. The physical meaning of the constructed solutions is visually represented through 3D and 2D graphs. The applied method proves to be useful in solving other fractional nonlinear evolution equations in natural and applied sciences.
Article
Materials Science, Multidisciplinary
Shao-Wen Yao et al.
Summary: In this paper, the solutions of DSWE and BLPE equations in the conformable sense are studied. The sine-cosine method is used to obtain various traveling wave solutions to the proposed nonlinear systems. The obtained results play an important role in elucidating some important nonlinear problems in applied sciences and engineering.
RESULTS IN PHYSICS
(2022)
Article
Engineering, Mechanical
Xing Lu et al.
Summary: Interaction solutions between lump and soliton in nonlinear partial differential equations are analyzed using Hirota bilinear forms. The one-lump-multi-stripe and one-lump-multi-soliton solutions can be generated from combined solutions, and necessary and sufficient conditions for the two types of interaction solutions are presented based on the associated bilinear equations. Applications are made for various (2+1)-dimensional equations.
NONLINEAR DYNAMICS
(2021)
Article
Optics
Pengfei Li et al.
Summary: This study investigates the existence, bifurcation, and stability of two-dimensional optical solitons in the context of the fractional nonlinear Schrodinger equation. Different scenarios of bifurcations are observed depending on the stability and type of nonlinearities, with asymmetric solitons emerging through symmetry breaking bifurcation. The restoration or destruction of symmetry in antisymmetric solitons can be controlled by adjusting the fractional diffraction in the case of self-defocusing saturable nonlinearity.
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, 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
Xing Lu et al.
Summary: (English Summary:)
The research investigates the integrability characteristics of the (2+1)-dimensional Kadomtsev-Petviashvili type equations, finding that the failure to pass the Painleve test is due to a non-vanishing compatibility condition at the highest resonance level. Soliton solutions and the N-soliton solution formula were derived and validated using the Hirota condition. The study also explores the criteria for the linear superposition principle and methods for generating resonant solutions, as well as deriving Backlund transformation, Lax pair, and infinitely many conservation laws through the Hirota bilinear method and Bell polynomial approach.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Materials Science, Multidisciplinary
Lanre Akinyemi et al.
Summary: This study investigates the perturbed nonlinear Schrodinger-Hirota equation with spatio-temporal dispersion using an improved Sardar sub-equation method, revealing various soliton solutions and demonstrating their dynamical behaviors and physical significance through different parameter values.
RESULTS IN PHYSICS
(2021)
Article
Physics, Multidisciplinary
Si-Jia Chen et al.
Summary: In this study, N-rational solutions to two (2+1)-dimensional nonlinear evolution equations were constructed using the long wave limit method, and M-lump solutions were derived by making certain parameters conjugate to each other. The properties of 1-, 2- and 3-lump solutions were presented and discussed, with focus on the unchanged amplitude and shape of the one lump wave during propagation. Analysis of the dynamic properties of collisions among multiple lump waves revealed the possibility of fusion and fission, with different paths followed based on parameters chosen. These results provide insights into nonlinear phenomena in optics, fluid dynamics, and plasma.
Article
Engineering, Mechanical
Ming-Ze Yin et al.
Summary: By utilizing the doubly interval-censored data model and the new ECIMM algorithm, this research estimated the parameters of the COVID-19 incubation period. It was found that a 14-day quarantine can largely interrupt transmission, but individuals requiring special monitoring should be isolated for about 20 days for safety, providing insights for epidemic prevention and control.
NONLINEAR DYNAMICS
(2021)
Article
Engineering, Mechanical
Xing Lu et al.
Summary: This paper proposes a novel two-stage epidemic model with a dynamic control strategy to describe the spread of COVID-19 in China. Through theoretical analysis and numerical simulations, the feasibility and effectiveness of the dynamic control strategy in combating the epidemic are verified.
NONLINEAR DYNAMICS
(2021)
Article
Physics, Multidisciplinary
Abdul-Majid Wazwaz
Article
Mathematics, Applied
Si-Jia Chen et al.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2020)
Article
Engineering, Mechanical
Chao-Qing Dai et al.
NONLINEAR DYNAMICS
(2020)
Article
Physics, Mathematical
Deng-Shan Wang et al.
REPORTS ON MATHEMATICAL PHYSICS
(2020)
Article
Engineering, Electrical & Electronic
Wen-Xiu Ma
OPTICAL AND QUANTUM ELECTRONICS
(2020)
Article
Mathematics, Applied
Wen-Xiu Ma
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2019)
Article
Mathematics, Applied
Wen-Xiu Ma
JOURNAL OF GEOMETRY AND PHYSICS
(2018)
Article
Mathematics, Applied
Mei-Juan Xu et al.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2016)
Article
Engineering, Mechanical
Xing Lu et al.
NONLINEAR DYNAMICS
(2016)
Article
Acoustics
V. A. Korneev et al.
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
(2014)
Article
Computer Science, Interdisciplinary Applications
Abdullahi Rashid Adem et al.
COMPUTERS & FLUIDS
(2013)
Article
Mathematics
N. H. Ibragimov et al.
RUSSIAN MATHEMATICAL SURVEYS
(2013)
Article
Physics, Multidisciplinary
Engui Fan
Article
Physics, Mathematical
Deng-Shan Wang et al.
JOURNAL OF MATHEMATICAL PHYSICS
(2010)
Article
Mathematics, Applied
SC Anco et al.
EUROPEAN JOURNAL OF APPLIED MATHEMATICS
(2002)
