Article
Mathematics, Applied
Lingfei Li, Yingying Xie, Liquan Mei
Summary: This study obtains multiple-order rogue waves through symbolic computation based on the generalized (2+1)-dimensional Kadomtsev-Petviashvili equation. The first order rogue wave's maximum and minimum values and trajectories are systematically discussed, while the second and third order rogue waves are established by eliminating the impact of the mixed partial derivative, and their temporal evolution is visualized through numerical simulations.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Engineering, Mechanical
Yu-Lan Ma, Abdul-Majid Wazwaz, Bang-Qing Li
Summary: In this paper, a new extended Kadomtsev-Petviashvili (eKP) equation is developed and its integrability is confirmed using Painleve analysis. Bilinear form, multiple soliton solutions and lump solutions are derived using Hirota's direct method, along with soliton, breather and lump interaction solutions. Graphs are used to illustrate the diverse dynamic behaviors of the obtained solutions.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
Lingfei Li, Yongsheng Yan, Yingying Xie
Summary: This paper proposes a new extended (3 + 1)-dimensional Kadomtsev-Petviashvili equation that describes a unique dispersion effect about x,z plane. Its integrability is confirmed via the WTC-Kruskal algorithm in Painleve sense. The paper systematically derives various soliton, breather, and solitary wave solutions of the equation and explores the rational and semi-rational solutions in the long wave limit.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Computer Science, Interdisciplinary Applications
Yingying Xie, Lingfei Li
Summary: This paper investigates a generalized (3+1)-dimensional Kadomtsev-Petviashvili Benjamin-Bona-Mahony equation describing fluid flow in offshore structures. Four kinds of rogue wave solutions, including a fourth order rogue wave solution, are constructed and systematically analyzed. The obtained rogue waves exhibit certain circularity structure and are shown to be stable during propagation.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Mathematics, Applied
Ling An, Chuanzhong Li
Summary: The paper studies a multicomponent weakly interacted generalized Kadomtsev-Petviashvili equation, deriving various types of equations by choosing different coefficients, and deducing its Backlund transformation and Hirota bilinear equations. By focusing on the two-component case, soliton and rogue wave solutions were solved in detail, with the rogue wave solutions showing distinct eye and butterfly shapes for the first and second components respectively.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Zhao Zhang, Biao Li, Junchao Chen, Qi Guo, Yury Stepanyants
Summary: This paper investigates the anomalous scattering of lumps within the Kadomtsev-Petviashvili equation. It is found that lumps of equal amplitudes can experience anomalously slow interactions and form stationary bound states. The asymptotic behavior of lumps is analyzed analytically and numerically, and the results are illustrated graphically. The approach introduced in this paper can be extended to other (2+1)-dimensional integrable systems.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Materials Science, Multidisciplinary
Israr Ahmad, Abdul Jalil, Aman Ullah, Shabir Ahmad, Manuel De la Sen
Summary: This paper focuses on extracting new exact solutions of a (4+1)-dimensional Davey-Stewartson-Kadomtsev-Petviashvili (DSKP) equation. The obtained solutions are in the form of exponential and trigonometric functions and show different types of wave solutions for specific parameter values.
RESULTS IN PHYSICS
(2023)
Article
Engineering, Mechanical
Abdul-Majid Wazwaz
Summary: This work introduces two extended KP equations and explores their integrability and solution properties through numerical and graphical analysis.
NONLINEAR DYNAMICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Jutong Guo, Jingsong He, Maohua Li, Dumitru Mihalache
Summary: The paper constructs multiple-order line rogue waves of extended Kadomtsev-Petviashvili equation using the Hirota bilinear method and symbolic computation approach. It analyzes the motion trajectories and extreme values of the first-order line rogue wave solutions in detail, and explicitly derives second-order and third-order line rogue waves, illustrating their complex dynamical behaviors through three-dimensional plots.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Computer Science, Interdisciplinary Applications
Yu-Lan Ma, Abdul-Majid Wazwaz, Bang-Qing Li
Summary: This paper presents a new (3+1)-dimensional integrable Kadomtsev-Petviashvili equation, whose integrability is confirmed through Painleve analysis. Various solutions including bilinear form, multiple-soliton, breather, and lump solutions are obtained using the Hirota bilinear method, revealing rich dynamical behaviors. Notably, splitting and fusing phenomena are observed when lump waves interact, offering insights into complex wave dynamics in fluids.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Engineering, Mechanical
Yuan Shen, Bo Tian, Chong-Dong Cheng, Tian-Yu Zhou
Summary: In this paper, an extended (3+1)-dimensional Kadomtsev-Petviashvili equation is investigated. The N-soliton solutions of the equation are determined using an existing bilinear form, and the Mth-order breather and Hth-order lump solutions are constructed from the N-soliton solutions using complex conjugated transformations and the long-wave limit method. The interactions between different solutions are studied, and it is found that the amplitudes, shapes, and velocities of the solitons, breathers, and lumps remain unchanged after the interactions, indicating elastic interactions.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Mechanical
Hajar F. Ismael, Tukur Abdulkadir Sulaiman, Harivan R. Nabi, W. Mahmoud, M. S. Osman
Summary: The purpose of this research is to investigate the variable coefficients Kadomtsev-Petviashvili equation, and successfully provide multiple soliton and M-lump solutions to this equation. The collision phenomena between these solutions are also studied. By employing appropriate parameter values, the physical characteristics of the results are emphasized using 3D and contour charts. The outcomes of this work reveal the physical characteristics of lump and lump interactions that occur in many dynamical regimes.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Mechanical
Lingfei Li, Yifan Nie, Minting Zhu, Yingying Xie
Summary: This paper obtains an exponential variable separation solution of an extended (3+1)-dimensional B-type Kadomtsev-Petviashvili equation using the projective Riccati equation method. The obtained solution covers many special cases and allows for the analysis of collision and wave motion characteristics between folded waves.
NONLINEAR DYNAMICS
(2023)
Article
Mechanics
Yu Chen, Xing Lue
Summary: This article discusses the Wronskian solutions to the B-type Kadomtsev-Petviashvili (BKP) equation based on the Plucker relation. Rational solutions, positon solutions, negaton solutions, and complexiton solutions to the BKP equation are directly constructed. The Wronskian formulation is used to generate rational solutions in the form of determinants, and a polynomial identity is demonstrated to show that a linear combination of two Wronskian polynomial solutions of different orders is again a solution to the bilinear BKP equation.
Article
Physics, Multidisciplinary
Muhammad Ahtisham Ilyas, Ahmad Javid, Abdul-Majid Wazwaz
Summary: In this paper, we investigate an extended (3+1)-dimensional B-type Kadomtsev-Petviashvili equation that has applications in various scientific fields. The integrability of the model is tested using Painleve analysis. Hirota's simplified technique is used to study the solutions of one, two, and three kink-solitons. By employing a dependent variable transformation, the bilinear form of the model is obtained, which is then used to analyze lump and lump interaction solutions with periodic and kink waves. The dynamics and characteristics of the obtained solutions are extensively studied using 3D and 2D graphs.
Article
Mathematics, Applied
Bang-Qing Li
Summary: This paper investigates a (2+1)-dimensional nonlinear ferromagnetic spin chain system with variable coefficients, proposing a new hybrid breather and rogue wave solution. Abundant interaction behaviors between the breather and rogue wave are observed by selecting variable coefficient functions and adjusting parameters.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2022)
Article
Mathematics, Applied
Yu-Lan Ma, Bang-Qing Li
Summary: In this work, the nonlocal Boussinesq equations are investigated and the soliton solutions are derived using the Hirota bilinear method. The multiple solitons are classified into two types based on system parameters, and stripe-like solitons and breathers are obtained. The bifurcation behavior of solitons is found to be nonlinear, with the existence of three-and four-leaf envelopes for the breathers.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Engineering, Mechanical
Yu-Lan Ma, Bang-Qing Li
Summary: In this work, soliton resonances in a transient stimulated Raman scattering system were studied. The multi-soliton solutions were obtained using the Darboux transformation technique. By controlling the eigenvalues of the vector matrices, interesting soliton resonances were observed. The resonant solitons exhibited unique geometric patterns and their distances could be controlled by phase parameters.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Mechanical
Bang-Qing Li, Yu-Lan Ma
Summary: By reconstructing the Darboux transformation to the Manakov system, new explicit solutions composed of a rogue wave and a breather for the system are obtained. The novel 'firewall' effect during the rogue wave and breather interactions is revealed, where the rogue wave and breather cannot cross over one another during the collision.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Bang-Qing Li, Yu -Lan Ma
Summary: This article investigates a complex short pulse system (CSPS) in optical-fiber communications with fast varying packets. New higher-order rogue wave solutions are constructed for the system using the Darboux transformation technique. Novel phase transitions from single-peak to multi-ring-folded rogue waves are observed by controlling the parameter. These results are helpful in understanding the formation mechanism of rogue wave compressions.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Engineering, Mechanical
Bang-Qing Li, Yu-Lan Ma
Summary: This article investigates the optical soliton resonances and soliton molecules in the Lakshmanan-Porsezian-Daniel system governed by a four-order nonlinear Schrodinger equation. Using the Darboux transformation method, the system's analytical multi-soliton solutions are obtained. New soliton resonances and soliton molecules are discovered for the system by manipulating the spectrum and phase parameters. The study reveals significant properties of the soliton resonances and soliton molecules in the system.
NONLINEAR DYNAMICS
(2023)
Article
Physics, Multidisciplinary
Bang-Qing Li, Yu -Lan Ma
Summary: In this letter, we investigate a (3+1)-dimensional nonlinear Geng equation. By applying the Hirota bilinear method, we obtain the one-to four-order solutions of the equation and identify novel phenomena, including hybrid soliton and breather waves, soliton molecules with corresponding constraints, and breather molecules. These findings are reported for the first time in the context of this equation.
Article
Mathematics, Applied
Yu-Lan Ma, Abdul-Majid Wazwaz, Bang-Qing Li
Summary: This work introduces a new (3+1)-dimensional Sakovich equation for describing nonlinear wave propagation. The Painlevé integrability of the equation is confirmed using the truncation expansion method. The general soliton solution and multiple-soliton solutions of the equation are constructed, and the equation is shown to possess soliton molecules. Several interesting features of the equation are also discovered.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2022)
Article
Engineering, Mechanical
Yu-Lan Ma, Bang-Qing Li
Summary: In this study, new explicit expressions for one- to four-order soliton solutions in the AB system are derived using the Darboux transformation scheme, and the existence of soliton resonances and soliton molecules is investigated. Two types of soliton resonances, local and global, are identified, and the evolution dynamics from local to global resonances are revealed. Furthermore, the presence of soliton molecules in the AB system is reported, and it is found that parallel soliton molecules without entanglement become global soliton resonances with entanglement as the phase parameters approach zero. These findings provide theoretical evidence for the breather-like wave structure in the system and contribute to our understanding of the AB system and how to manage and control these stable resonant solitons.
NONLINEAR DYNAMICS
(2023)
Article
Optics
Sathishkumar Perumal, Bang-Qing Li, Arul Varman Kesavan
Summary: We numerically investigate the propagation of optical soliton under the influence of higher-order nonlinearities in the anomalous dispersion regime. The complex cubic-quintic Ginzburg-Landau equation, a generalized nonlinear Schrodinger equation, is solved to consider nonlinear gain-absorption processes, higher-order correction term to the intensity-dependence of refractive index, and intra-pulse Raman scattering. Through numerical simulation, we find that higher-order dispersive term and nonlinearities can perturb a soliton, resulting in a rich variety of soliton phenomena such as period-doubling bifurcation, Raman-induced spectral shifts, multi-branch pulsating solitons, and pulsating solitons with different periodicity.
Article
Physics, Multidisciplinary
Bang-Qing Li, Yu-Lan Ma
Summary: This paper presents a systematic study on breathers of the AB system in fluids. The expressions of first to third-order breather solutions are explicitly computed using the Darboux transformation method. Some new and interesting features are discovered, including Ak-breathers and Ma-breathers. Additionally, the system exhibits novel spatio-temporal patterns for the periodical wave packets forming the breathers, such as two-petals, three-petals, and four-petals. The interactions between two or multiple breathers are found to be elastic, and various interaction patterns are observed, such as Ak-breathers and Ma-breathers crossing vertically or parallel with the same speed.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Engineering, Mechanical
Yu-Lan Ma, Abdul-Majid Wazwaz, Bang-Qing Li
Summary: This study presents a systematic investigation of the soliton interaction dynamics in the Maccari system. By using the bilinear method, explicit first- and second-order solutions are derived, and various soliton interaction phenomena are observed, including soliton resonances, soliton molecules, soliton oscillations, and heterotypic solitons. Importantly, it is found that soliton molecules and heterotypic solitons exhibit different characteristics under different coordinate systems.
NONLINEAR DYNAMICS
(2023)
Article
Optics
Yu-Lan Ma, Bang-Qing Li
Summary: This article investigates a defocusing Lakshmanan-Porsezian-Daniel optical (DLPD) system with higher-order dispersion and higher-order nonlinear effects. New analytical solutions for the system are obtained using the Darboux transformation method. Novel intersection solitons and their characteristics are found under certain parameter setting. Four basic soliton structures are identified: (i) bright-dark soliton with reduced amplitude at the intersection point; (ii) bright-dark soliton with increased amplitude at the intersection point; (iii) doubly-bright soliton with bright peaks; (iv) doubly-dark soliton with dark troughs. Moreover, the complexity of the structures at the intersection point increases with the order of the solutions, indicating that this system can carry more optical information by exciting higher order solitons.
Article
Physics, Multidisciplinary
Bang-Qing Li, Yu-Lan Ma
Summary: In this article, we explore the new features of the Caudrey-Dodd-Gibbon (CDG) equation arising from fluid mechanism. We introduce a constant in the transformation to link the solution and auxiliary function defined in the bilinear form. By constructing different auxiliary functions, we obtain the breather solution, one- to three-soliton solutions, and lump wave solution. We discover the generation of a breather from a stripe-like soliton as well as soliton molecules and their interaction, where the maximum amplitude decreases with overlap. We also observe unique features of this equation, such as having only two-soliton molecules, not N (N ≥ 3)-soliton molecules, and a line-like lump wave parallel to the x-axis, not the t-axis.
Article
Mathematics, Applied
Yu-Lan Ma, Bang-Qing Li
Summary: This article investigates the dynamical interaction behavior of a short pulse equation in optical fibers with fast-varying packets, discovering the interaction dynamics between solitons, breathers, and their hybrid forms. The first- to fourth-order solutions are explicitly calculated using the bilinear method. The solutions are categorized into three classes based on their dispersion coefficients: stripe-loop-like soliton, breather, and their hybrid form. The existence of bright and dark solitons is observed. Additionally, a breather may consist of periodical peak-trough waves and periodical kink-loop-like waves. As the order of the solutions increases, there are abundant and complicated interaction behaviors for the solitons, breathers, and their hybrid forms due to these rich patterns.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Physics, Multidisciplinary
Tinggui Chen, Baizhan Xia, Dejie Yu, Chuanxing Bi
Summary: This study proposes a gradient phononic crystal structure for enhanced acoustic sensing. By breaking the symmetry of the PC structure, topologically protected edge states are introduced, resulting in topological acoustic rainbow trapping. The robustness and enhancement properties are verified numerically and experimentally.
