Article
Engineering, Mechanical
Yujie Sun, Biao Li
Summary: Anomalously interacting lump patterns of the (2+1)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili equation can be generated through normally interacting lump chains using N-soliton solutions of Hirota's bilinear method. There are two different paths to generate these patterns.
NONLINEAR DYNAMICS
(2023)
Article
Materials Science, Multidisciplinary
S. Liu, Z. Yang, A. Althobaiti, Y. Wang
Summary: In the field of nonlinear sciences, soliton theory is considered as a significant and effective area of research. This study focuses on obtaining lump and lump-type solutions to the generalized water wave equation using Hirota's bilinear method. The solutions obtained include various forms of interaction, such as quadratic, hyperbolic cosine and exponential, and quadratic term with Jacobi elliptic functions. Graphical representations of collision solutions of the equation are also provided. The employed technique in this study has not been applied to the main equation in the existing literature, making the findings valuable for investigating analytical solutions to other nonlinear equations.
RESULTS IN PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
Wenting Li, Ailing Jiao
Summary: In this article, a new dynamical system equation named the (3+1)-dimensional Hirota-bilinear-like equation is constructed. The new equation has more nonlinear terms but maintains the same bilinear form as the original equation. The generalized Hirota bilinear operator and its logarithmic transformation are used to obtain the new equation and find its solutions. Symbolic solutions including lump solutions and lump-kink-type rogue wave solutions are obtained, and the shapes and movements of these solutions are analyzed through simulation of the propagation of lump waves and the interaction between lump-type waves and two-kink soliton waves.
RESULTS IN PHYSICS
(2023)
Article
Mathematics, Applied
Wenxia Chen, Ru Guan, Minjie Dong, Lixin Tian, Jingjie Ma
Summary: In this paper, the bilinear form of the Boussinesq equation is investigated using the Hirota bilinear method. The N-solitons solution and lump solution are obtained based on the presented bilinear form. Graphical analyses and establishment of new interactive solutions further enhance the understanding of the dynamic behavior of soliton and lump solutions of the equation.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2022)
Article
Engineering, Mechanical
Xing Lu, Si-Jia Chen
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
Physics, Applied
Hongcai Ma, Shupan Yue, Aiping Deng
Summary: This paper investigates the exact solutions of the (2 + 1)-dimensional combined pKP-BKP equation, obtaining lump, lump-soliton, and breather wave solutions through different function combinations, and presenting the dynamic properties of these solutions.
MODERN PHYSICS LETTERS B
(2022)
Article
Thermodynamics
Abdul-Majid Wazwaz
Summary: This study aims to introduce a variety of integrable Boussinesq equations with distinct dimensions and explores lump solutions that are rationally localized in all directions in space using the simplified Hirota's method and lump schemes. The author confirms the lump solutions for every model illustrated by graphical representations and examines their features. Various lump solutions are presented by using different numerical values of the included parameters, providing useful algorithms for using symbolic computation with Maple for the determination of lump solutions.
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
(2022)
Article
Physics, Multidisciplinary
Wenxia Chen, Yi Wang, Lixin Tian
Summary: In this paper, we explored the exact solutions to the fourth-order extended (2+1)-dimensional equation, including lump solution, periodic cross-kink solutions, and bright-dark soliton solution. By calculating and plotting, we observed the dynamics of the solutions under different parameters.
COMMUNICATIONS IN THEORETICAL PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
Shao-Wen Yao, Md Nuruzzaman, Dipankar Kumar, Nishat Tamanna, Mustafa Inc
Summary: This study derives lump solutions for a new integrable (3 + 1)-dimensional Boussinesq equation and its dimensionally reduced equations using the Hirota bilinear method and Maple. The derived lump solutions display two trough positions and one crest position, with the amplitudes and shapes of the lump waves remaining constant during propagation but changing their positions. Graphical outputs of the propagations of the obtained lump wave solutions illustrate the changes in trough and crest positions over time with constant velocity, with the free parameters of the model playing a significant role in altering the shapes and amplitudes of the waves.
RESULTS IN PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
Deniu Yang, Xujie Jiang
Summary: In this paper, we investigate the (2+1)-dimensional generalized Hirota-Satsuma-Ito equation with time-dependent properties, which is useful in describing the propagation of shallow water waves. By utilizing the bilinear formalism and symbolic computation, we obtain several solutions including line-soliton, lump, one-lump-one-stripe, and one-lump-one-soliton using different ansatze's functions. To analyze the dynamics, we utilize various plots. These obtained solutions are reliable in the fields of mathematical physics and engineering.
RESULTS IN PHYSICS
(2023)
Article
Multidisciplinary Sciences
Alexander Alexandrov
Summary: In this note, it is proved that any tau-function of the KdV hierarchy can also solve the BKP hierarchy after rescaling the times.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2021)
Article
Physics, Applied
Wen-Xiu Ma, Solomon Manukure, Hui Wang, Sumayah Batwa
Summary: Through the Hirota bilinear formulation, a (2+1)-dimensional combined fourth-order nonlinear equation with lump solutions is proposed, presenting two classes of lump solutions explicitly in terms of the coefficients in the equation. A set of equations examples are provided to demonstrate the diversity of the considered combined nonlinear equation, along with three-dimensional plots, x-curves, and y-curves of two specific lump solutions in two cases of the combined equation.
MODERN PHYSICS LETTERS B
(2021)
Article
Materials Science, Multidisciplinary
Shaofu Wang
Summary: The Hirota bilinear method is used to construct the new dynamics of complex N-soliton solutions for a nonlocal breaking equation. By using an auxiliary traveling wave function, different-order soliton solutions, bifurcation solutions, and lump solutions of the model are obtained. The physical phenomena and soliton propagation behavior of these solutions are explored, and the proposed soliton solutions are verified.
RESULTS IN PHYSICS
(2022)
Article
Physics, Multidisciplinary
Kai-Zhong Shi, Shou-Feng Shen, Bo Ren, Wan-Li Wang
Summary: A new (2+1)-dimensional higher-order extended asymmetric Nizhnik-Novikov-Veselov (eANNV) equation is proposed by introducing additional bilinear terms and utilizing independent transformations. The dynamics of the solutions are illustrated using specific parameter choices and graphical plots.
COMMUNICATIONS IN THEORETICAL PHYSICS
(2022)
Article
Engineering, Mechanical
Marwan Alquran, Tukur Abdulkadir Sulaiman, Abdullahi Yusuf, Ali S. Alshomrani, Dumitru Baleanu
Summary: This work establishes lump periodic and exact traveling wave solutions for the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation using the Hirota bilinear method and robust integration techniques. The innovative solutions provide insights into specific physical difficulties and have proven useful in long-wave and high-power communications networks. The results depict new features and reflect previously unknown physical dynamics for the governing model.
NONLINEAR DYNAMICS
(2023)
