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
Materials Science, Multidisciplinary
Shafiq Ahmad, Aman Ullah, Shabir Ahmad, Sayed Saifullah, Ali Shokri
Summary: The aim of this paper is to study new exact solutions of the Davey-Stewartson-Kadomtsev-Petviashvili (DSKP) equation using the modified tanh method and a new Ricatti equation. The results demonstrate the existence of periodic singular and nonsingular solitons for specific parameter values. The solutions are plotted and presented in 3D and density graphs, and Mathematica is used for computation and simulations.
RESULTS IN PHYSICS
(2023)
Article
Engineering, Aerospace
Alexis S. Truitt, Christine M. Hartzell
Summary: Research has shown that subcentimeter debris poses a significant threat to Earth-orbiting spacecraft sensors and subsystems. These debris can generate plasma density solitary waves, or solitons, detectable by ground- and space-based sensors. Three-dimensional simulations of orbital debris solitons will aid in the design of future detection methods, allowing for collision-free mapping of small debris populations.
JOURNAL OF SPACECRAFT AND ROCKETS
(2021)
Article
Physics, Multidisciplinary
I. S. Elkamash, I Kourakis
Summary: The study focuses on the propagation properties of a two-dimensional ion-acoustic wavepacket in a magnetized quantum plasma, deriving a Zakharov-Kuznetsov (ZK) equation with explicit stationary solutions and analyzing the influence of various plasma configuration parameters on electrostatic solitary wave characteristics. The stability of the pulse soliton solution of the ZK equation is investigated and found to be unstable to oblique perturbations. The dependence of the instability growth rate on plasma composition parameters is also discussed, providing insights into nonlinear excitations in dense astrophysical plasma environments.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)
Article
Physics, Mathematical
Bao Wang, Zhiqiang Chen
Summary: This paper investigates the breather, lump, and interaction solutions of the (2+1)-dimensional generalized Kadomtsev-Petviashvili equation with a small perturbation. High-order periodic breather solutions are obtained using Hirota's bilinear method, and general lump solutions and mixed solutions to the gKP equation are generated by combining the long wave limit methods and module resonance constraints. The space-time structures of the breather solutions, lump solutions, and interaction solutions are investigated and discussed.
ADVANCES IN MATHEMATICAL PHYSICS
(2022)
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
Andrei K. Pogrebkov
Summary: The paper introduces a new hierarchy directed to negative numbers of times, derived based on the commutator identities. This approach enables the introduction of linear differential equations that can be transformed into nonlinear integrable ones through a special dressing procedure.
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
Mechanics
O. Kaptsov, D. O. Kaptsov
Summary: This paper calculates a group of point transformations admitted by the three-dimensional Kadomtsev-Petviashvili equation, gives an example of an invariant solution, and reveals exact solutions for the equation in the form of double waves. The resulting solutions, expressed in terms of elementary functions, describe an interaction between a pair of solitons. Smooth bounded rational solutions are also constructed.
JOURNAL OF APPLIED MECHANICS AND TECHNICAL PHYSICS
(2021)
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, Applied
S. Ryskamp, M. A. Hoefer, G. Biondini
Summary: This study investigates the interaction of an oblique line soliton with a one-dimensional dynamic mean flow using the Kadomtsev-Petviashvili II (KPII) equation. By deriving invariant quantities and positing the initial configuration as a Riemann problem, quantitative predictions are made regarding the evolution of the line soliton within the mean flow. The interaction between the oblique soliton and changing mean flow leads to novel features not observed in the reduced problem, and gives rise to all three possible types of two-soliton solutions of the KPII equation.
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
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
Physics, Multidisciplinary
Hongcai Ma, Nan Su, Aiping Deng
Summary: In this paper, the (2+1)-dimensional combined potential Kadomtsev-Petviashvili with B-type Kadomtsev-Petviashvili equation is studied. Auto-Backlund transformations are obtained in two cases based on the extended homogeneous balancing method. Various explicit solutions of this equation are derived using these transformations. Complexiton solutions composed of exponential, hyperbolic, and trigonometric solutions are obtained from the Hirota bilinear form of this equation through the extended transformed rational function method. One-kink and two-kink soliton solutions are derived by Maple symbolic calculation, and the breather-wave solution is obtained via the extended homoclinic test approach. Additionally, 3D graphics and density plots are depicted to illustrate the dynamical features of the obtained solutions.
Article
Mechanics
Chong-Dong Cheng, Bo Tian, Tian-Yu Zhou, Yuan Shen
Summary: In this paper, a (3 + 1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili (GVCKP) equation in a fluid or plasma is investigated. The Nth-order Wronskian solutions for that equation are derived and proved under certain variable-coefficient constraints, where N is a positive integer. One-, two-, and three-soliton solutions in the Wronskian for that equation are given. By means of the Pfaffianization procedure, a coupled (3 + 1)-dimensional GVCKP system is constructed from that equation. Bilinear form for that coupled system is exported. Under certain variable-coefficient constraints, those Wronski-type and Gramm-type Pfaffian solutions for that coupled system are obtained and proved with the help of the Pfaffian identities.
