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Extraction of newly soliton wave structure to the nonlinear damped Korteweg–de Vries dynamical equation through a computational technique
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Extraction of newly soliton wave structure to the nonlinear damped Korteweg–de Vries dynamical equation through a computational technique
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Extraction of newly soliton wave structure to the nonlinear damped Korteweg–de Vries dynamical equation through a computational technique
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Journal Article
Extraction of newly soliton wave structure to the nonlinear damped Korteweg–de Vries dynamical equation through a computational technique
2024
Overview
The damped Korteweg-de Vries (D-KdV) equation is a significant extension of the Korteweg–de Vries equation, which plays an important role in understanding the complex dissipative wave system. This study explores the historical evolution and mathematical properties of the damped KdV equation. The auxiliary equation approach is utilized on nonlinear damped KdV equation to extract the newly exact solitary wave results. New solutions are extracted in bright solitons, kink wave solitons, mixed dark-bright solitons, anti-kink wave solitons, periodic solitons, dark solitons, and solitary wave structures. The physical behavior of secured solutions are visualizing in contour, 3-D, and 2-D plots based on numerical simulation with the computational software Mathematica. The proposed approach is employed, offering a powerful mathematical tool for analyzing the effects of damping on wave dynamics. Through this investigation, the study sheds light on the captivating interplay between physics and mathematics in the realm of wave phenomena. These newly constructed solutions are important in nonlinear acoustics, optical fiber, nonlinear optics, soliton wave theory, plasma physics, and ion acoustic wave phenomena. As a result, our proposed method is directed, concise, and practical for various kinds of nonlinear evolution equations.
Publisher
Springer US
