Modulational instability and mixed breather–lump interaction solutions in the (2+1)-dimensional KMN equation

This article studies diverse forms of lump-type solutions for coupled nonlinear generalized Zakharov equations (CNL-GZEs) in plasma physics through an appropriate transformation approach and bilinear equations. By utilizing the positive quadratic assumption in the bilinear equation, the lump-type solutions are derived. Similarly, by employing a single exponential transformation in the bilinear equation, the lump one-soliton solutions are derived. Furthermore, by choosing the double exponential ansatz in the bilinear equation, the lump two-soliton solutions are found. Interaction behaviors are observed and we also establish a few new solutions in various dimensions (3D and contour). Furthermore, we compute rogue-wave solutions and lump periodic solutions by employing proper hyperbolic and trigonometric functions.

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“…Now, to obtain the LP solution, the functions p and q in Equations ( 3) and ( 4) are assumed to be [27,28],…”

Section: Lump Solutionmentioning

confidence: 99%

“…To obtain the lump one-strip solution, we use the transformations given in Equations ( 3) and ( 4) [22,[27][28][29][30]:…”

Section: Lump One-strip Soliton Interaction Solutionmentioning

confidence: 99%

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Lump-Type Solutions, Lump Solutions, and Mixed Rogue Waves for Coupled Nonlinear Generalized Zakharov Equations

2023

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“…Some potential scholars have recently solved several well-known NLEEs to find solutions using the HBT. For instance, the (3+1)-dimensional YTSF system 27 , the (3+1)-dimensional BKP-Boussinesq model 28 , the (2+1)-dimensional Burgers model 29 , the (3+1)-dimensional gKPB model 30 and many more 31 , 32 .…”

Section: Introductionmentioning

confidence: 99%

The dynamical perspective of soliton solutions, bifurcation, chaotic and sensitivity analysis to the (3+1)-dimensional Boussinesq model

Nadeem,

Islam,

Şenol

et al. 2024

Sci Rep

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In this study, we examine multiple perspectives on soliton solutions to the (3+1)-dimensional Boussinesq model by applying the unified Riccati equation expansion (UREE) approach. The Boussinesq model examines wave propagation in shallow water, which is derived from the fluid dynamics of a dynamical system. The UREE approach allows us to derive a range of distinct solutions, such as single, periodic, dark, and rational wave solutions. Furthermore, we present the bifurcation, chaotic, and sensitivity analysis of the proposed model. We use planar dynamical system theory to analyze the structure and characteristics of the system’s phase portraits. The current study depends on a dynamic structure that has novel and unexplored results for this model. In addition, we display the behaviors of associated physical models in 3-dimensional, density, and 2-dimensional graphical structures. Our findings demonstrate that the UREE technique is a valuable mathematical tool in engineering and applied mathematics for studying wave propagation in nonlinear evolution equations.

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“…In 2015, an effective algebraic method to obtain lump solutions of integrable systems was proposed by Ma [1]. Subsequently, He also provided theoretical support for this method and proved it [2], which made great progress in the solution of lump wave and attracted the attention of a large number of researchers, such as Tian [3][4][5], Lü [6][7][8], He [9][10][11], Wen [12][13][14], Su [15][16][17], Lan [18][19][20], Chen [21][22][23] et al…”

Section: Introductionmentioning

confidence: 99%

Different wave structures for a new extended shallow water wave equation in (3+1) dimension

Liu,

Zhu

2024

Preprint

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In this work, a new extended shallow water wave equation in (3+1) dimensions is studied, which represents abundant physical meaning in nonlinear shallow water wave. We discuss the interaction between lump wave and single solitary wave, which is an inelastic collision. Further, the interaction between lump wave and two solitary waves, and the interaction between lump wave and periodic wave are also studied. Finally, the interaction among lump, periodic and one solitary waves is investigated. The dynamic properties of the obtained results are shown and analyzed by some three-dimensional images.

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Modulational instability and mixed breather–lump interaction solutions in the (2+1)-dimensional KMN equation

Cited by 8 publications

References 48 publications

Lump-Type Solutions, Lump Solutions, and Mixed Rogue Waves for Coupled Nonlinear Generalized Zakharov Equations

Lump-Type Solutions, Lump Solutions, and Mixed Rogue Waves for Coupled Nonlinear Generalized Zakharov Equations

The dynamical perspective of soliton solutions, bifurcation, chaotic and sensitivity analysis to the (3+1)-dimensional Boussinesq model

Different wave structures for a new extended shallow water wave equation in (3+1) dimension

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