Bilinear form and Pfaffian solutions for a (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics and plasma physics

Article Engineering, Mechanical

Painleve integrability and lump solutions for two extended (3+1)- and (2+1)-dimensional Kadomtsev-Petviashvili equations

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)

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Article Physics, Multidisciplinary

Oceanic shallow-water symbolic computation on a (2+1)-dimensional generalized dispersive long-wave system

Xin-Yi Gao et al.

Summary: This study focuses on certain dispersive long gravity waves on the shallow water of an open ocean. A (2+1)-dimensional generalized dispersive longwave system is examined, involving wave height and horizontal velocity. Symbolic calculations provide two sets of hetero-Backlund transformations and two sets of similarity reductions. Each set results in a known (2+1)-dimensional Broer-Kaup-Kupershmidt system or a known ordinary differential equation, relying on the coefficients of the original system.

PHYSICS LETTERS A (2023)

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Article Mathematics

Molecules and New Interactional Structures for a (2+1)-Dimensional Generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt Equation

Yan Li et al.

Summary: Soliton molecules (SMs) of the (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt (gKDKK) equation are discovered using a velocity resonance ansatz. These solitons can transform into asymmetric solitons by adjusting certain parameters. Additionally, a breather degeneration approach can be used to construct a double-peaked lump solution. By applying a mixed technique of a resonance ansatz and conjugate complexes of partial parameters to multisoliton solutions, various types of interactional structures are formed, including soliton molecules (SM), breather molecules (BM), and soliton-breather molecules (SBM). Graphical investigation and theoretical analysis demonstrate that the interactions involving SM, BM, and SBM are inelastic.

ACTA MATHEMATICA SCIENTIA (2023)

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Article Engineering, Mechanical

N-fold Darboux transformation and solitonic interactions for the Kraenkel-Manna-Merle system in a saturated ferromagnetic material

Yuan Shen et al.

Summary: In this paper, the Kraenkel-Manna-Merle system for ultra-short waves in a saturated ferromagnetic material is investigated, and three- and four-fold solutions of the system are derived via N-fold Darboux transformation. The interaction among the solitons is graphically depicted, providing insights into certain nonlinear phenomena in ferromagnetic materials.

NONLINEAR DYNAMICS (2023)

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Article Mathematics, Interdisciplinary Applications

Novel trial functions and rogue waves of generalized breaking soliton equation via bilinear neural network method

Run-Fa Zhang et al.

Summary: In this work, new test functions are constructed by setting generalized activation functions in different artificial network models. The explicit solution of a generalized breaking soliton equation is solved using the bilinear neural network method. Rogue waves of the generalized breaking soliton equation are obtained using symbolic computing technology and displayed intuitively with the help of Maple software.

CHAOS SOLITONS & FRACTALS (2022)

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Article Physics, Applied

Multiple exact solutions for the dimensionally reduced p-gBKP equation via bilinear neural network method

Run-Fa Zhang et al.

Summary: In this paper, new trial functions are constructed based on the bilinear neural networks method, and multiple solutions of the dimensionally reduced p-generalized Burgers-Kadomtsev-Petviashvili equation are solved. The dynamic properties of the solutions are analyzed with appropriate parameters and different activated functions.

MODERN PHYSICS LETTERS B (2022)

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Article Engineering, Mechanical

Bilinear residual network method for solving the exactly explicit solutions of nonlinear evolution equations

Run-Fa Zhang et al.

Summary: In this study, a bilinear residual network method is proposed to solve nonlinear evolution equations. The method reduces the complexity of the model and provides more interactive results. The exact analytical solution for the Caudrey-Dodd-Gibbon-Kotera-Sawada-like equation is obtained using the steps of solving through the residual network. Characteristic plots and dynamic analysis of these rogue waves are given.

NONLINEAR DYNAMICS (2022)

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Article Engineering, Mechanical

Painleve analysis, auto-Backlund transformation and analytic solutions of a (2+1)-dimensional generalized Burgers system with the variable coefficients in a fluid

Tian-Yu Zhou et al.

Summary: This paper investigates a (2+1)-dimensional generalized Burgers system with variable coefficients in a fluid. It obtains the Painleve-integrable constraints of the system with respect to the variable coefficients. Based on truncated Painleve expansions, an auto-Backlund transformation is constructed, along with soliton solutions. Multiple kink solutions are derived using truncated Painleve expansions. Breather solutions, half-periodic kink solutions, and hybrid solutions composed of breathers and kink waves are obtained via complex-conjugate transformation.

NONLINEAR DYNAMICS (2022)

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Article Physics, Applied

Soliton molecule and their interaction solutions for the (2+1)-dimensional gKDKK equation

Shengwan Fan et al.

Summary: (English Summary:) In this paper, the N-soliton solution of the (2 + 1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt equation is constructed using the Backlund transformation, Hirota bilinear method, and an auxiliary function. The solutions include line soliton molecule, lump, and breather solutions. Explicit expressions for soliton molecules, including combinations of line solitons with breathers or lumps, can also be obtained. Interaction solutions among soliton molecules, lumps, and breathers are achieved. The paper introduces the concepts of velocity resonance, module resonance of wavenumber, and the long-wave limit.

INTERNATIONAL JOURNAL OF MODERN PHYSICS B (2022)

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Article Physics, Applied

Rogue waves, classical lump solutions and generalized lump solutions for Sawada-Kotera-like equation

Run-Fa Zhang et al.

Summary: In this study, the (2 + 1)-dimensional Sawada-Kotera-like (SK-like) equation is derived and three trial functions are constructed using 3-2 and 3-2-2 neural network models. By giving specific parameters, classic lump, generalized lump solutions, and new rogue wave solutions are obtained, which are intuitively displayed through various curve plots of three-dimensional contour plotting.

INTERNATIONAL JOURNAL OF MODERN PHYSICS B (2022)

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Article Engineering, Mechanical

Hybrid localized wave solutions for a generalized Calogero-Bogoyavlenskii-Konopelchenko-Schiff system in a fluid or plasma

Peng-Fei Han et al.

Summary: This paper investigates hybrid localized wave solutions with different forms for the generalized Calogero-Bogoyavlenskii-Konopelchenko-Schiff system using the long wave limit method and complex conjugate condition technique. Four kinds of bilinear auto-Backlund transformations are constructed by constructing different equivalent exchange formulas. Three-dimensional diagrams are drawn to better analyze the dynamic characteristics of the solutions. Seven kinds of combined waves are summarized, including the hybrid solutions consisting of L-order kink waves, Q-order breather waves, and M-order lump waves.

NONLINEAR DYNAMICS (2022)

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Article Engineering, Mechanical

Fission and fusion solutions of the (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt equation: case of fluid mechanics and plasma physics

Hongcai Ma et al.

Summary: This study focuses on the fission and fusion solutions of the (2+1)-dimensional gKDKK equation. Numerical simulations and density diagrams are used to investigate the interactions of various molecules with y-type molecules. The findings suggest that the shape of y-type molecules remains unchanged and no energy change occurs during their interaction with other molecules.

NONLINEAR DYNAMICS (2022)

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Article Engineering, Mechanical

Wronskian, Gramian, Pfaffian and periodic-wave solutions for a (3+1)-dimensional generalized nonlinear evolution equation arising in the shallow water waves

Fei-Yan Liu et al.

Summary: In this paper, a (3+1)-dimensional generalized nonlinear evolution equation for shallow water waves is investigated. Nth-order solutions are proved to exist and soliton solutions are constructed. One-periodic-wave solutions are also derived, and the relationship between these solutions is explored. The equation is further simplified to a two-dimensional dynamic system, and the phase portraits of the system are given based on a qualitative analysis.

NONLINEAR DYNAMICS (2022)

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Article Engineering, Mechanical

Dynamics of invariant solutions of mKdV-ZK arising n a homogeneous magnetised plasma

Raj Kumar et al.

Summary: In this study, classical Lie symmetry analysis is used to obtain a new variety of similarity solutions for a nonlinear equation. Through comparison with previous results, the physical significance of these solutions is validated. Animation profiles reveal the dynamical behavior of these solutions, highlighting their importance for further research in this field.

NONLINEAR DYNAMICS (2022)

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Article Engineering, Mechanical

Nonlinear superposition between lump and other waves of the (2+1)-dimensional generalized Caudrey-Dodd-Gibbon-Kotera-Sawada equation in fluid dynamics

Hongcai Ma et al.

Summary: By introducing a novel constraint, this paper investigates the nonlinear superposition between one lump and other types of localised waves in the (2+1)-dimensional generalized Caudrey-Dodd-Gibbon-Kotera-Sawada (gCDGKS) equation. The results show that there is no interaction between the lump wave and line solitons, breather waves, and resonant Y-type solitons. Furthermore, the study defines novel velocity resonance constraints, ensuring that different types of localised waves have the same velocity magnitude and direction. This research provides important references for understanding certain nonlinear phenomena in fields such as shallow water waves, solitons, and fluid mechanics.

NONLINEAR DYNAMICS (2022)

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Article Engineering, Mechanical

Studies on certain bilinear form, N-soliton, higher-order breather, periodic-wave and hybrid solutions to a (3+1)-dimensional shallow water wave equation with time-dependent coefficients

Yuan Shen et al.

Summary: In this paper, we investigate a (3+1)-dimensional shallow water wave equation with time-dependent coefficients and obtain various solutions and their associated nonlinear phenomena using the Hirota method and symbolic computation.

NONLINEAR DYNAMICS (2022)

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Article Optics

Optical envelope soliton solutions for coupled nonlinear Schrodinger equations applicable to high birefringence fibers

Abdul-Majid Wazwaz et al.

Summary: This work investigates a two coupled nonlinear Schrodinger equation (CNLSE) applicable to high birefringence fibers. Various ansätze are used to derive bright and dark optical envelope soliton solutions, as well as solutions with distinct structures such as periodic, exponential, and singular. The analysis reveals the significant contribution of nonlinear terms to pulse compression feature and nonlinear birefringence phenomena.

OPTIK (2022)

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Article Multidisciplinary Sciences

Lie Symmetries, Closed-Form Solutions, and Various Dynamical Profiles of Solitons for the Variable Coefficient (2+1)-Dimensional KP Equations

Sachin Kumar et al.

Summary: This investigation focuses on two novel Kadomtsev-Petviashvili (KP) equations with time-dependent variable coefficients that describe the nonlinear wave propagation of small-amplitude surface waves in narrow channels or large straits. The obtained variable coefficient solutions are more relevant and useful for understanding the dynamical structures of nonlinear KP equations and shallow water wave models.

SYMMETRY-BASEL (2022)

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Article Engineering, Mechanical

Lump, soliton, and interaction solutions to a generalized two-mode higher-order nonlinear evolution equation in plasma physics

Sachin Kumar et al.

Summary: This article investigates a generalized two-mode evolution equation and examines its soliton solutions and interactions using logarithmic transformation and the Hirota method. The equations have applications in various real-life examples.

NONLINEAR DYNAMICS (2022)

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Article Mathematics, Applied

Auto-Backlund transformations, Lax pair, bilinear forms and bright solitons for an extended (3+1)-dimensional nonlinear Schrodinger equation in an optical fiber

Tian-Yu Zhou et al.

Summary: In this Letter, we investigate an extended (3+1)-dimensional nonlinear Schrodinger equation in an optical fiber. The auto-Backlund transformations and a Lax pair are obtained under certain optical-fiber coefficient constraints. Bilinear forms, bright two-soliton, and bright three-soliton solutions are derived using the Hirota method under certain optical-fiber coefficient constraints.

APPLIED MATHEMATICS LETTERS (2022)

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Article Optics

Bright and dark optical solitons for (3+1)-dimensional hyperbolic nonlinear Schrodinger equation using a variety of distinct schemes

Abdul-Majid Wazwaz et al.

Summary: The current study aims to derive a class of bright soliton and dark soliton solutions for the (3 + 1)-dimensional hyperbolic nonlinear Schrodinger equation. Various schemes are utilized to obtain a variety of optical soliton solutions, including bright and dark solitons. Additionally, the study reveals a new class of solutions with distinct structures, such as periodic, complex, and exponential solutions. These findings contribute to the understanding of optical properties.

OPTIK (2022)

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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)

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Article Engineering, Electrical & Electronic

On integrability of an extendedBogoyavlenskii-Kadomtsev-Petviashviliequation: Multiple soliton solutions

Abdul-Majid Wazwaz

Summary: In this paper, an extended Bogoyavlenskii-Kadomtsev-Petviashvili (eBKP) equation was constructed and its integrability was justified using Painleve analysis. Multiple soliton solutions were derived using Hirota's direct method, and a variety of exact solutions including singular kink solutions, periodic solutions, and exponential solutions were also obtained.

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING-ELECTRONIC NETWORKS DEVICES AND FIELDS (2021)

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Article Engineering, Mechanical

Rogue wave solutions and the bright and dark solitons of the (3+1)-dimensional Jimbo-Miwa equation

Run-Fa Zhang et al.

Summary: The neural network model for the (3+1)-dimensional Jimbo-Miwa equation was extended to a 4-2-3 model in this paper. By introducing specific activation functions, a new test function was constructed to obtain analytical solutions, including rogue wave solutions and bright and dark solitons. The dynamical characteristics of these waves were exhibited through curve plots, three-dimensional plots, contour plots, and density plots.

NONLINEAR DYNAMICS (2021)

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Article Physics, Applied

Lie symmetry analysis, optimal system and conservation law of a generalized (2+1)-dimensional Hirota-Satsuma-Ito equation

Sheng-Nan Guan et al.

Summary: This paper investigates a generalized (2+1)-dimensional Hirota-Satsuma-Ito (GHSI) equation using Lie symmetry approach. The study identifies some symmetries and similarity solutions, demonstrates the nonlinear self-adjointness of the equation, and constructs conservation laws based on Lie point symmetries and nonlinear self-adjointness. Additionally, physically meaningful solutions are illustrated graphically with appropriate parameter choices.

MODERN PHYSICS LETTERS B (2021)

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Article Engineering, Mechanical

Rogue and semi-rogue waves defined by volume

A. Ankiewicz

Summary: By defining a quantized nonlinear pulse volume, we can identify the characteristic of a possible rogue wave by examining its volume through a surface integral. If higher powers are needed in the integrand due to slow decay of a pulse, we refer to the excitation as a 'semi-rogue' wave.

NONLINEAR DYNAMICS (2021)

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Article Physics, Applied

Multiple rogue and soliton wave solutions to the generalized Konopelchenko Dubrovsky Kaup Kupershmidt equation arising in fluid mechanics and plasma physics

Onur Alp Ilhan et al.

Summary: Multiple rogue wave solutions and novel multiple soliton solutions of the generalized Konopelchenko-Dubrovsky-KaupKupershmidt equation were constructed using the bilinear method and specific activation functions. Analytical solutions were obtained through symbolic computation with Maple 18 software. Exact lump and rogue wave solutions were constructed by solving under-determined nonlinear system of algebraic equations, and their dynamical characteristics were exhibited through various three-dimensional plots.

MODERN PHYSICS LETTERS B (2021)

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Article Engineering, Mechanical

Bilinear form, soliton, breather, hybrid and periodic-wave solutions for a (3+1)-dimensional Korteweg-de Vries equation in a fluid

Chong-Dong Cheng et al.

Summary: This paper investigates a (3+1)-dimensional Korteweg-de Vries equation in a fluid, obtaining bilinear form, N-soliton solutions, and higher-order breather solutions. The effects of alpha, beta, gamma, and delta on the amplitude of the second-order breather are discussed. Hybrid solutions comprising the breathers and solitons are derived via the N-soliton solutions.

NONLINEAR DYNAMICS (2021)

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Article Mathematics, Applied