Article
Materials Science, Multidisciplinary
S. T. R. Rizvi, Aly R. Seadawy, S. K. Naqvi, Saeed Althubiti
Summary: This paper studies various analytical solutions of Atangana conformable Boussinesq-like equations (NLACBEs), including multi-wave solutions, rogue waves, M-shaped rational solutions, etc. By analyzing the unknown nonlinear confirmable differential equations, the relationship between lump interaction with kink, periodic cross-kink, and other types of exact solutions is computed. The graphical representation of the obtained analytical solutions shows the behavior of effective waves.
RESULTS IN PHYSICS
(2022)
Article
Multidisciplinary Sciences
Md. Emran Ali, Farjana Bilkis, Gour Chandra Paul, Dipankar Kumar, Hasibun Naher
Summary: The study examines lump, one-stripe, lump-stripe, and breather wave solutions to the (2+1)-dimensional Sawada-Kotera equation using the Hirota bilinear method. Different functions are assumed for the unknown function to obtain solutions, and the propagations and interaction behaviors of the solutions are illustrated through graphical illustrations under various parameter selections. The outcomes provide insights into the physical nature of long waves in shallow water under gravity.
Article
Mathematics, Applied
Jian-Guo Liu, Abdul-Majid Wazwaz
Summary: The study focuses on a new (3 + 1)-dimensional equation, exploring various solutions such as lump solutions, interaction solutions between different waves, and breather wave solutions. Graphical representations of all solutions are presented in 3D and contour plots.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Interdisciplinary Applications
Sarfaraz Ahmed, Aly R. Seadawy, Syed T. R. Rizvi, Umar Raza
Summary: This paper examines the propagation of M-shape solitons and their interactions with kink waves in the (2 + 1)-dimensional integrable Schwarz-Korteweg-de Vries problem, using symbolic computation with ansatz functions technique and logarithmic transformation. The study of these waves has significant applications in fluid dynamics, nonlinear optics, climate science, and other fields.
FRACTAL AND FRACTIONAL
(2023)
Article
Engineering, Electrical & Electronic
Syed T. R. Rizvi, Aly R. Seadawy, Ali Nimra, Ali Ahmad
Summary: The analytical rational solitons of the Kraenkel-Manna-Merle (KMM) system in a saturated ferromagnetic material are studied using symbolic computation with ansatz functions and logarithmic transformation. Various systematic solutions are explored, including lump soliton, rogue wave, lump with one kink, multiwave, periodic wave, periodic cross-kink wave, and breather lump wave. The stability and structure of these solutions are analyzed, and the results are presented in tables.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Physics, Mathematical
Yinghui He
Summary: In this paper, the localized properties and interaction solutions of a new extended Jimbo-Miwa (EJM) equation are studied. The exact solutions of the EJM equation, including lump soliton solution, lump-kink soliton solution, and periodic lump solution, are obtained using the Hirota bilinear method and the test function method. The dynamic properties of the obtained solutions are also discussed by graphical simulation. To the best of our knowledge, these results have not been reported before.
ADVANCES IN MATHEMATICAL PHYSICS
(2023)
Article
Physics, Applied
S. T. R. Rizvi, Aly R. Seadawy, S. Ahmed, M. Younis, K. Ali
Summary: This study addresses four main inducements (lump, rogue wave, Homoclinic breather, and multi-wave solutions) for the (2+1)-Modified Veronese Web (MVW) equation using Hirota bilinear approach and ansatz technique. By assuming different forms of the function f in the Hirota bilinear form, the study successfully prevented lump, rogue wave, breather, and multi-wave solutions. A precise compatible wave transformation was utilized to obtain multi-wave solutions, and the motion tracks of lump, rogue wave, and multi-waves were explained both physically and theoretically, providing new insights into the qualitative features of wave phenomena.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2021)
Article
Engineering, Electrical & Electronic
Syed T. R. Rizvi, Aly R. Seadawy, Samia Ahmed, Azhar Bashir
Summary: In this article, we explore soliton solutions, breathers, and rational solutions for the nonlinear Schrodinger equation with quadratic nonlinear susceptibility. Various types of solutions, such as lump wave solutions, interaction between periodic and kink waves, and multiwave solutions, are discussed. We also investigate the stability of these solutions and represent them graphically.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Materials Science, Multidisciplinary
Na Yuan
Summary: In this paper, a new (3+1)-dimensional equation is studied, focusing on the interaction solutions of lump and N-soliton. The interaction solution among lump wave, 1-soliton and periodic wave is presented, and a breather-wave solution is obtained. The dynamical behavior is shown through abundant 3D, density and contour plots.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Applied
Qianqian Li, Wenrui Shan, Panpan Wang, Haoguang Cui
Summary: This paper investigates a (2+1)-dimensional coupled nonlinear partial differential equation with variable coefficients in an inhomogeneous medium. The breather wave solutions and lump solutions are constructed using the extended homoclinic breather technique and the generalized positive quadratic function method. Hirota bilinear method is also applied to find N-soliton wave solutions. Improved results for special equations with different coefficients are obtained. The dynamic behaviors of different types of solutions are analyzed through plotting their images.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Engineering, Mechanical
Abdullahi Yusuf, Tukur Abdulkadir Sulaiman, Ali S. Alshomrani, Dumitru Baleanu
Summary: (English Summary:)
In this paper, breather wave and lump periodic wave solutions for the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada system are established using the Hirota bilinear approach. The existence circumstances of these novel solutions are described in detail. The research on these solutions is helpful in explaining unique physical challenges and has advantages in the transmission of long-wave and high-power communications networks.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Peng-Fei Wei, Chun-Xiao Long, Chen Zhu, Yi-Ting Zhou, Hui-Zhen Yu, Bo Ren
Summary: The (2+1)-dimensional Korteweg-de Vries-Sawada-Kotera-Ramani (KdVSKR) equation, composed of the KdV equation and the SK equation, is studied. Soliton molecules and multi-breather solutions are analyzed, showing the importance of phase values in determining the characteristics of these solutions. The interactions between soliton molecules and other structures are also investigated, revealing elastic collisions between them.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Thermodynamics
Na Liu
Summary: This paper studies the homoclinic breather waves, rogue waves, and multi-soliton waves of the (2 + 1)-dimensional Mel'nikov equation using Hirota's bilinear method, extended homoclinic test approach, and parameter limit method. The results show that these solutions exhibit dynamic properties vividly through figures, enriching the diversity of the dynamics of the (2 + 1)-dimensional Mel'nikov equation.
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
(2021)
Article
Engineering, Mechanical
Marwan Alquran, Rahaf Alhami
Summary: In this paper, Hirota's bilinear method is implemented to study the generalized perturbed-KdV equation, considering the test function approaches. Novel solutions are obtained and graphical analysis is conducted to show the physical structures of the solutions. Additionally, this work corrects previous published results and investigates the effects of nonlinearity, perturbation, and dispersion parameters on the propagation of the perturbed KdV.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Mechanical
Long-Xing Li
Summary: A (3+1)-dimensional generalized shallow water waves equation is investigated using different methods. N-soliton solutions, T-breathers, rogue waves, and M-lump solutions are derived through degeneration and parameter limit methods. Furthermore, hybrid solutions composed of soliton, breather, and lump are found during the partial degeneration process of N-soliton.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Applied
Jian-Guo Liu, Abdul-Majid Wazwaz
Summary: The study focuses on a new (3 + 1)-dimensional equation, exploring various solutions such as lump solutions, interaction solutions between different waves, and breather wave solutions. Graphical representations of all solutions are presented in 3D and contour plots.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Physics, Applied
Aly R. Seadawy, Khalid K. Ali, Jian-Guo Liu
Summary: This paper examines the Fokas-Lenells equation (FLE) for the propagation of ultra-short pulses in visual fibers, beyond the terms necessary for the nonlinear Schrodinger equation. The model includes spatio-temporal dispersal and self-steepening terms, and deep visual solutions of the FLE are discussed using the modified Kudryashov method and the extended tanh expansion method.
MODERN PHYSICS LETTERS B
(2021)
Article
Engineering, Multidisciplinary
Na Yuan, Jian-Guo Liu, Aly R. Seadawy, Mostafa M. A. Khater
Summary: The study focuses on a generalized variable-coefficient Kadomtsev-Petviashvili equation with self-consistent sources, investigating various wave solutions and interactions between waves. The interaction phenomenon of waves is demonstrated through 3D and contour plots.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2022)
Article
Physics, Multidisciplinary
Jian-Guo Liu, Huan Zhao
Summary: In this work, multiple rogue wave solutions of the generalized (2+1)-dimensional Camassa-Holm-Kadomtsev-Petviashvili equation are studied using symbolic computation approach. Examples of 1-rogue wave, 3-rogue wave, and 6-rogue wave solutions are presented, which are not found in other literature. Dynamic features of the obtained multiple rogue wave solutions are shown using 3D, contour, and density graphics.
CHINESE JOURNAL OF PHYSICS
(2022)
Article
Physics, Multidisciplinary
Jian-Guo Liu, M. S. Osman
Summary: Abundant nonautonomous solutions with different wave structures of a 3D variable-coefficient generalized shallow water wave equation are presented based on three-wave method. The dynamic properties of these solutions, including the mutation of basic configurations of nonautonomous waves over time, are demonstrated and analyzed graphically. Discussions also focus on the interaction between different types of waves, such as lump waves, resonance stripe solitons, periodic waves, and breather-type periodic solitons.
CHINESE JOURNAL OF PHYSICS
(2022)
Article
Engineering, Mechanical
Wen-Hui Zhu, Fei-Yan Liu, Jian-Guo Liu
Summary: In this paper, a (4+1)-dimensional Kadomtsev-Petviashvili equation with variable coefficients in fluid mechanics is investigated. The lump, lump-soliton, and rogue-soliton solutions are obtained using the improved positive quadratic function method. The interaction between the lump wave and periodic wave is studied, and breather wave solutions are presented. The nonlinear dynamics of different nonautonomous wave structures solutions are described in 3D and contour plots.
NONLINEAR DYNAMICS
(2022)
Article
Physics, Mathematical
Chun-Rong Qin, Jian-Guo Liu, Wen-Hui Zhu, Guo-Ping Ai, M. Hafiz Uddin
Summary: In this article, we investigate a (2+1)-dimensional Korteweg-de Vries equation and obtain abundant periodic wave solutions using Hirota's bilinear form and a direct test function. The interaction solutions between lump and periodic waves, as well as among lump, periodic, and solitary waves, are presented. Additionally, we propose new double periodic-soliton solutions based on the extended homoclinic test technique. Furthermore, 3D and density plots are simulated and displayed to demonstrate the dynamic behavior of these obtained solutions.
ADVANCES IN MATHEMATICAL PHYSICS
(2022)
Article
Materials Science, Multidisciplinary
Chun-Rong Qin, Jian-Guo Liu
Summary: An improved test function method is proposed and successfully applied to solve the variable-coefficient Kadomtsev-Petviashvili equation, which describes waves in ferromagnetic media and matter-wave pulses in Bose-Einstein condensates.
RESULTS IN PHYSICS
(2022)
Article
Materials Science, Multidisciplinary
Mei Yang, Jian-Guo Liu
Summary: This paper investigates the wave solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov equations, including breather wave solutions, double-periodic soliton solutions, and interaction solutions of lump and periodic waves. Specific examples are used to illustrate the dynamic behaviors of nonlinear waves.
RESULTS IN PHYSICS
(2022)
Article
Materials Science, Multidisciplinary
Jian-Guo Liu, Hajar F. Ismael, Hasan Bulut
Summary: The aim of this study is to construct novel solutions for a new extension of the shallow water model in (3+1)-dimensions. A class of solutions, including multiple soliton solutions, breather wave, and mixed breather-soliton solutions, were obtained using simplified Hirota's method and a long-wave method. These solutions have important implications for predicting and modeling various environmental phenomena such as floods, tsunamis, and flow in rivers and open channels.
RESULTS IN PHYSICS
(2022)
Article
Optics
Wen-Hui Zhu, Jian-Guo Liu
Summary: In this study, a fifth-order nonlinear Schrodinger equation with variable coefficients is investigated to understand the diffusion of ultrashort pulses in incompatible optical fibers. Non-traveling wave bright and dark soliton solutions are obtained using two direct functions. Additionally, non-traveling wave hyperbolic-type and trigonometric-type solutions are studied using the G'/G-expansion method. Dynamic properties and characteristics of these derived results are demonstrated using three-dimensional figures and contour figures.
Article
Mathematics, Applied
Yulei Cao, Hao Tian, Abdul-Majid Wazwaz, Jian-Guo Liu, Zhao Zhang
Summary: This paper introduces the PT-symmetric version of the (3+1)-dimensional nonlocal Mel'nikov equation and presents general soliton solutions, including crossed and parallel solitons, using the KP hierarchy reduction method. It also constructs semi-rational solutions consisting of lumps and solitons, which exhibit elastic collision. Additionally, a new method to obtain rational solutions of the Mel'nikov equation is given by reducing the semi-rational solutions of the (3+1)-dimensional nonlocal Mel'nikov equation. These novel dynamics have not been reported in (3+1)-dimensional nonlocal systems, expanding our research field and inspiring exploration of the mysteries of higher-dimensional nonlocal systems.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2023)
Article
Mathematics, Applied
Jian-Guo Liu, Abdul-Majid Wazwaz, Run-Fa Zhang, Zhong-Zhou Lan, Wen-Hui Zhu
Summary: This paper investigates a (3+1)-dimensional generalized breaking soliton equation in nonlinear media. The interaction solution between lump wave and N-soliton (N = 2, 3, 4) is derived. The interaction solution between lump wave and periodic waves is also studied. Breather-wave and multi-wave solutions are obtained. The dynamical behavior is demonstrated by 3D graphics and density plots. Via mathematical induction, the exact solution containing three arbitrary functions is also obtained.
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION
(2022)
Article
Physics, Multidisciplinary
Wen-Hui Zhu, M. Raheel, Jian-Guo Liu
Summary: This research investigates the impact of new optical solitons on the time-fractional integrable generalized (2+1)-dimensional nonlinear Schrodinger system with truncated M-fractional derivative. The obtained results demonstrate that these methods are efficient, straightforward, and reliable.
Article
Mathematics, Applied
Jian-Guo Liu, Abdul-Majid Wazwaz, Wen-Hui Zhu
Summary: This work examines variable-coefficient nonlinear evolution equations, which are often more suitable for describing complex physical models than constant coefficient models. A modified ansatz with variable coefficients is used to study the interaction between solitary and lump waves in these equations. The variable-coefficient Kadomtsev-Petviashvili equation is discussed to achieve this objective, and lump wave and interaction solutions are presented for this model. Three-dimensional plots and corresponding contour plots illustrate the dynamical behaviors of the obtained solutions by choosing appropriate values of the variable coefficients.
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION
(2022)
