Article
Engineering, Mechanical
Yulei Cao, Jingsong He, Yi Cheng
Summary: A new (3 + 1)-dimensional integrable KP equation is derived from a specific reduction of the (4 + 2)-dimensional KP equation in Fokas et al. (Fractal Fract 6:425, 2022). In this paper, the Wronskian and Grammian solutions of this o3 thorn 1THORN-dimensional integrable KP equation are proposed based on Pl_ucker relation and the Jacobi identity for determinants. Furthermore, three types of semi-rational solutions of this equation, namely (i) a hybrid of one lump and one soliton, (ii) a hybrid of multiple lumps and one soliton, and (iii) a hybrid of multiple lumps and multiple solitons, are proposed and their novel dynamics are discussed.
NONLINEAR DYNAMICS
(2023)
Article
Physics, Multidisciplinary
Zhao Zhang, Biao Li, Abdul-Majid Wazwaz, Qi Guo
Summary: This study focuses on a lump molecule obtained for the Kadomtsev-Petviashvili I system based on a reduced version of the Grammian form. It provides explicit coordinates of lump waves in molecules to accurately describe their asymptotic behavior. The dynamics and interactions of lump molecules are meticulously studied through asymptotic analysis, numerical calculations, and images, deepening the understanding of how lump waves can move along curves and change velocities at any time.
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
Mathematics
Gui Mu, Yan Zhu, Tingfu Feng
Summary: In this work, we utilize a variable separation approach to derive novel exact solutions for a (2+1)-dimensional Boussinesq-Kadomtsev-Petviashvili equation. By introducing two variable-separated arbitrary functions, we obtain new soliton excitations and localized structures. It is observed that the interaction between two solitons leads to the generation of large amplitude waves.
Article
Mathematics, Applied
T. S. Moretlo, A. R. Adem, B. Muatjetjeja
Summary: The study investigates a generalized (1 + 2)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili (BKP) equation, an augmented form of existing equations, for evolutionary shallow-water waves. By utilizing new methods, novel exact solutions are obtained that can effectively mimic the dynamics of complex waves in fluids.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Applied
Guangfu Han, Xinyue Li, Qiulan Zhao, Chuanzhong Li
Summary: This paper investigates the (2+1)-dimensional Kadomtsev-Petviashvili I (KP I) equation, which can be reduced to a (1+1)-dimensional system consisting of a generalized nonlinear Schrodinger (NLS) equation and a modified Korteweg-de Vries (mKdV) equation using constraints. The generalized (m, N - m)-fold Darboux transformation is used to explore various solutions, including single structure solutions and interaction solutions of arbitrary structures formed based on single structure solutions. The obtained structure solutions are discussed analytically and shown graphically, providing insight into the interaction phenomena of localized nonlinear waves in the KP I equation.
PHYSICA D-NONLINEAR PHENOMENA
(2023)
Article
Mathematics, Applied
Wenxia Chen, Ru Guan, Lixin Tian
Summary: In this paper, we investigated lump soliton solutions and breather solutions for the (3+1)-dimensional Kadomtsev-Petviashvili equation using the Hirota direct method and Maple symbolic computation. We also provided plots of the solutions to better understand their dynamic behavior.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Engineering, Mechanical
Lingfei Li, Yongsheng Yan, Yingying Xie
Summary: In this study, a variable separation solution for a new extended B-type Kadomtsev-Petviashvili equation is derived using the multi-linear variable separation approach. The obtained solutions contain two arbitrary functions without any constraint. Various folded solitary waves are also derived by introducing a multi-valued function. Additionally, the chase-collision and interaction phenomena are observed by adjusting the velocities.
NONLINEAR DYNAMICS
(2022)
Article
Physics, Applied
Pei Xia, Yi Zhang, Heyan Zhang, Yindong Zhuang
Summary: This paper investigates the behavior of rogue lumps on a background of kink waves for the Bogoyavlenskii-Kadomtsev-Petviashvili equation, and obtains a new family of determinant semi-rational solutions through the Kadomtsev-Petviashvili hierarchy reduction method combined with the Hirota bilinear method. It is found that rogue lumps arise from the kink waves background and eventually decay back to the background as truly localized lumps.
MODERN PHYSICS LETTERS B
(2022)
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
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
Yong-Li Sun, Jing Chen, Wen-Xiu Ma, Jian-Ping Yu, Chaudry Masood Khalique
Summary: In this paper, the localized solutions of the (2+1)-dimensional B-Kadomtsev-Petviashvili (BKP) equation are further studied using the theory of Hirota bilinear operator, which include N-soliton solutions, M-lump solutions, higher-order breathers and hybrid solutions. The dynamic behaviors of these solutions are analyzed and shown graphically through numerical simulations with specific parameters.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
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
Mathematics, Applied
Weaam Alhejaili, Mohammed. K. Elboree, Abdelraheem M. Aly
Summary: This work investigates the multi-rogue-wave solutions for the Kadomtsev-Petviashvili (KP) equation in two (3+1)-dimensional extensions. The symbolic computation approach and special polynomials developed from the Hirota bilinear equation are utilized. The first, second, and third-order rogue wave solutions for these equations are derived. The physical properties and interactions of multiple rogue waves are analyzed and visualized. The obtained results are significant for understanding the dynamics of higher-order rogue waves in the deep ocean and nonlinear optical fibers.
Article
Engineering, Mechanical
Zhonglong Zhao, Lingchao He
Summary: In this paper, the Grammian solution of the Kadomtsev-Petviashvili I equation is used to investigate a new type of multiple-lump solution. The interaction solutions between multiple-lump waves and line solitons are constructed using nonzero constant matrices and a non-homogeneous polynomial. Numerical simulations are used to investigate the interactions among the multiple lumps and between lumps and solitons, extending the understanding of the dynamics of the Kadomtsev-Petviashvili I equation.
NONLINEAR DYNAMICS
(2022)
Article
Physics, Multidisciplinary
Chuanjian Wang, Hui Fang
Article
Mathematics, Interdisciplinary Applications
Chuanjian Wang, Hui Fang
Article
Physics, Multidisciplinary
Yvye Wang, Changzhao Li, Chuanjian Wang, Jianping Shi, Zhangxiang Liu
Summary: In this paper, the exact solutions and soliton diffusion phenomenon of two kinds of stochastic KdV equations with variable coefficients are considered. The exact solutions are obtained by using symmetric reduction, generalized wave transformation, and the Clarkson-Kruskal direct method. Numerical simulations are provided to demonstrate the effectiveness of the analytic methods and the results show that the soliton diffusion phenomenon is influenced by noise.
