4.5 Article

Wave solutions to the more general (2+1)-dimensional Boussinesq equation arising in ocean engineering

Related references

Note: Only part of the references are listed.
Article Mathematics, Applied

Breather, lump and N-soliton wave solutions of the (2+1)-dimensional coupled nonlinear partial differential equation with variable coefficients

Qianqian Li et al.

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 Mathematics, Applied

Lump and lump-multi-kink solutions in the (3+1)-dimensions

Si-Jia Chen et al.

Summary: Based on the test function method, this paper presents the necessary and sufficient conditions for deriving lump solutions to special types of (3+1)-dimensional nonlinear evolution equations. Two approaches to construct lump multi-kink solutions are proposed. The existence of lump solutions and lump-multi-kink solutions is illustrated with examples. These methods are of significance for studying the existence of lump solutions and mixed solutions.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2022)

Article Physics, Multidisciplinary

On dynamical behavior for optical solitons sustained by the perturbed Chen-Lee-Liu model

Sibel Tarla et al.

Summary: This study investigates the perturbed Chen-Lee-Liu model and its solutions for the propagation of an optical pulse in plasma and optical fiber. The generalized exponential rational function method is applied to obtain non-trivial solutions such as optical singular, periodic, hyperbolic, exponential, and trigonometric soliton solutions. The results demonstrate that this method is effective and simple for solving nonlinear engineering and physical problems, with the obtained solutions exhibiting rich dynamical evolutions important in practical applications.

COMMUNICATIONS IN THEORETICAL PHYSICS (2022)

Article Engineering, Electrical & Electronic

New bidirectional wave solutions with different physical structures to the complex coupled Higgs model via recent ansatze methods: applications in plasma physics and nonlinear optics

Marwan Alquran et al.

Summary: This study highlights the concept of bidirectional-wave solutions through studying the complex coupled Higgs model, and presents the physical structures of bidirectional isolated-wave solutions through graphical analysis.

OPTICAL AND QUANTUM ELECTRONICS (2022)

Article Materials Science, Multidisciplinary

Inelastic soliton wave solutions with different geometrical structures to fractional order nonlinear evolution equations

M. Adel et al.

Summary: This article investigates the applications of the general time fractional Burger-Fisher (TF-BF) and the space-time regularized long-wave (STF-RLW) equations in cold plasma as well as in areas related to nonlinear science and engineering. The equations are transformed to ordinary differential equations (ODEs) using a fractional complex transform and the characteristics of confirmable fractional derivative (CFD). The extended tanh-function (ETF) approach is then utilized to find various analytical solutions with different geometrical wave structures for these models.

RESULTS IN PHYSICS (2022)

Article Materials Science, Multidisciplinary

A new extended (2+1)-dimensional Kadomtsev-Petviashvili equation with N-solitons, periodic solutions, rogue waves, breathers and lump waves

Lingfei Li et al.

Summary: In this study, a new extended integrable (2+1)-dimensional Kadomtsev-Petviashvili equation is proposed and investigated to model slowly varying perturbation waves in dispersion fluids. Various types of solutions, including soliton solutions, periodic solutions, breather solutions, and mixed solutions, have been derived using different methods.

RESULTS IN PHYSICS (2022)

Article Materials Science, Multidisciplinary

Cubic splines solutions of the higher order boundary value problems arise in sandwich panel theory

Aasma Khalid et al.

Summary: This article presents an innovative strategy using cubic splines to solve 14th-order nonlinear boundary value problems. By transforming the problems into a system of linear equations and utilizing both cubic polynomial spline and cubic non-polynomial spline, accurate solutions and derivative estimates are obtained.

RESULTS IN PHYSICS (2022)

Article Mathematics

Lump Collision Phenomena to a Nonlinear Physical Model in Coastal Engineering

Tukur Abdulkadir Sulaiman et al.

Summary: This study investigates a dimensionally nonlinear evolution equation using the integrable shallow water wave-like equation and the Hirota bilinear approach to obtain lump solutions, exploring their interaction with other solutions. Novel results including lump-periodic, two wave, and breather wave solutions are obtained and their propagation features are depicted. The physical quantities and attributes of nonlinear waves are found to be related to parameter values.

MATHEMATICS (2022)

Article Optics

Optical soliton solutions of variable coefficient Biswas-Milovic (BM) model comprising Kerr law and damping effect

Lakhveer Kaur et al.

Summary: This course of research focuses on the Biswas-Milovic (BM) model with variable coefficients, including the Kerr law and damping effect. The Biswas-Milovic (BM) equation provides a mathematical framework for describing soliton transmission via optical wave guides in a more general sense. By employing different ansatz techniques and time-dependent coefficients, bright, dark, and singular soliton solutions to the governing equation have been successfully obtained. The acquired solutions are presented through various appealing figures, reflecting the potential characteristics of such solitons.

OPTIK (2022)

Article Physics, Multidisciplinary

Analysis of parametric effects in the wave profile of the variant Boussinesq equation through two analytical approaches

Shao-Wen Yao et al.

Summary: The improved Bernoulli subequation function (IBSEF) method and the new auxiliary equation (NAE) technique are introduced to establish general and specific solutions. The physical significance of the obtained solutions is speculated by depicting the 3D profiles and interpreting the physical incidents. The obtained solutions and graphical representations visualize the dynamics of the phenomena.

OPEN PHYSICS (2022)

Article Physics, Multidisciplinary

Einstein's vacuum field equation: Painleve analysis and Lie symmetries

Lakhveer Kaur et al.

Summary: This study investigates Einstein's vacuum field equation through Painleve analysis and auto-Backlund transformation, aiming to explore movable critical points and point symmetries. The results reveal that the symmetries of the equation form an infinite-dimensional Lie algebra, with acquired solutions containing arbitrary functions and parameters.

WAVES IN RANDOM AND COMPLEX MEDIA (2021)

Article Engineering, Mechanical

Dynamics of optical solitons and nonautonomous complex wave solutions to the nonlinear Schrodinger equation with variable coefficients

Tukur Abdulkadir Sulaiman et al.

Summary: The study focuses on a nonlinear variable coefficients Schrodinger's equation with spatio-temporal dispersion in Kerr law media, aiming to construct novel solutions using a complex amplitude ansatz scheme. Bright and combined dark-bright optical solitons are successfully revealed, along with two nonautonomous complex wave solutions in dark and bright optical solitons forms. The impact of variable coefficients on the reported results is clearly shown in 3-dimensional and contour graphs.

NONLINEAR DYNAMICS (2021)

Article Materials Science, Multidisciplinary

Construction of multi-wave complexiton solutions of the Kadomtsev-Petviashvili equation via two efficient analyzing techniques

Abdullahi Yusuf et al.

Summary: In this study, the (2+1)-dimensional Kadomtsev-Petviashvili equation is investigated using the three-waves method, with multi-waves solutions and exponential function solutions successfully extracted. The physical features of the results are further demonstrated through interaction phenomenon shown in 3-dimensional and contour plots, all of which have been tested to satisfy the original nonlinear partial differential equation.

RESULTS IN PHYSICS (2021)

Article Physics, Multidisciplinary

Solitonic fusion and fission for a (3+1)-dimensional generalized nonlinear evolution equation arising in the shallow water waves

Yuan Shen et al.

Summary: This study investigates a (3 + 1)-dimensional generalized nonlinear evolution equation in shallow water waves and obtains X-type, Y-type, and periodic lump-stripe soliton solutions through symbolic computation and the Hirota method. Fusion and fission phenomena are observed in the X-type soliton solutions, while the fission phenomenon is observed in the Y-type soliton solutions. The interaction between periodic lump and stripe solitons is found to be inelastic.

PHYSICS LETTERS A (2021)

Article Mathematics, Applied

A computational approach for shallow water forced Korteweg-De Vries equation on critical flow over a hole with three fractional operators

Pundikala Veeresha et al.

Summary: The study focuses on analyzing the behaviors of forced KdV equation using q-homotopy analysis transform technique, showing reliable results for both integer and fractional order models. The combination of q-homotopy analysis scheme and Laplace transform proves to be an effective approach for solving the problem.

INTERNATIONAL JOURNAL OF OPTIMIZATION AND CONTROL-THEORIES & APPLICATIONS-IJOCTA (2021)

Article Engineering, Electrical & Electronic

Optical bidirectional wave-solutions to new two-mode extension of the coupled KdV-Schrodinger equations

Marwan Alquran

Summary: In this work, a new two-mode extension to the coupled KdV-Schrodinger equations is presented, which describes the propagation and interaction of symmetric bidirectional solitary-waves. The celebrated Kudryashov-expansion method is used to find explicit solutions to the model, which are then analyzed and physical properties are drawn through 2D and 3D plots.

OPTICAL AND QUANTUM ELECTRONICS (2021)

Article Materials Science, Multidisciplinary

Physical properties for bidirectional wave solutions to a generalized fifth-order equation with third-order time-dispersion term

Marwan Alquran

Summary: In this work, the physical-structure propagations of a generalized fifth-order nonlinear equation involving time-dispersion term are studied, which is recently proposed by Wazwaz. Three functional methods are implemented to seek solitary wave solutions, and 2D-plots are provided to recognize the type of the obtained solutions. Finally, some physical properties of the bidirectional waves that such model admits are proposed.

RESULTS IN PHYSICS (2021)

Article Physics, Multidisciplinary

Three-wave interactions in a more general (2+1)-dimensional Boussinesq equation

Dan Zhao et al.

EUROPEAN PHYSICAL JOURNAL PLUS (2020)

Article Mathematics, Interdisciplinary Applications

A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment

Sunil Kumar et al.

CHAOS SOLITONS & FRACTALS (2020)

Article Mathematics, Applied

Fundamental solutions of anomalous diffusion equations with the decay exponential kernel

Xiao-Jun Yang et al.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2019)

Article Materials Science, Multidisciplinary

A study of optical wave propagation in the nonautonomous Schrodinger-Hirota equation with power-law nonlinearity

M. S. Osman et al.

RESULTS IN PHYSICS (2019)

Article Mathematics, Applied

Two-soliton solution to a generalized KP equation with general variable coefficients

Mingliang Wang et al.

APPLIED MATHEMATICS LETTERS (2018)

Article Engineering, Electrical & Electronic

The dynamical behavior of mixed-type soliton solutions described by (2+1)-dimensional Bogoyavlensky-Konopelchenko equation with variable coefficients

M. S. Osman et al.

JOURNAL OF ELECTROMAGNETIC WAVES AND APPLICATIONS (2018)

Article Physics, Multidisciplinary

A new nonlinear integrable fifth-order equation: multiple soliton solutions with unusual phase shifts

Abdul-Majid Wazwaz et al.

PHYSICA SCRIPTA (2018)

Article Engineering, Mechanical

Abundant interaction solutions of the KP equation

Jin-Yun Yang et al.

NONLINEAR DYNAMICS (2017)

Article Materials Science, Multidisciplinary

Exact solutions of (3

Syed Tauseef Mohyud-Din et al.

RESULTS IN PHYSICS (2017)

Article Engineering, Mechanical

Lump solutions to dimensionally reduced -gKP and -gBKP equations

Wen Xiu Ma et al.

NONLINEAR DYNAMICS (2016)

Article Physics, Multidisciplinary

Lump solutions to the Kadomtsev-Petviashvili equation

Wen-Xiu Ma

PHYSICS LETTERS A (2015)

Article Mathematics, Applied

Solving the (3+1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm

Wen-Xiu Ma et al.

APPLIED MATHEMATICS AND COMPUTATION (2012)