Nonlinear wave dynamics in dispersive media: analytical insights from the nonlinear modified generalized Vakhnenko equation

Dan Chen; Dan Chen

doi:10.3934/math.2025734

AIMS Mathematics

2025, Volume 10, Issue 7: 16407-16413. doi: 10.3934/math.2025734

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Nonlinear wave dynamics in dispersive media: analytical insights from the nonlinear modified generalized Vakhnenko equation

Dan Chen ^,

College of Computer Science, Chengdu University, Chengdu 610106, China

Received: 27 April 2025 Revised: 16 July 2025 Accepted: 17 July 2025 Published: 22 July 2025
MSC : 34G20, 35C05, 35C07

This investigation explores the nonlinear modified generalized Vakhnenko (NMGV) equation, a pivotal model of nonlinear wave interactions within nonlinear dispersive media. The equation represents an extension of the classical Vakhnenko framework, integrating higher-order nonlinearities that significantly impact wave propagation. Comprehending these effects is essential for propelling the advancement of nonlinear wave theory in mathematical physics and engineering contexts. Utilizing the Khater Ⅲ method, we derive exact solutions that encapsulate the salient features of the NMGV equation's wave configurations. The research unveils innovative soliton-like solutions, shedding light on the intricate nonlinear mechanisms at play. These findings underscore the efficacy of the proposed methodology in addressing intricate nonlinear systems and highlight its applicability to analogous nonlinear evolution equations. By introducing novel analytical solutions, this study enriches the comprehension of dispersive wave phenomena and offers valuable insights for future research in nonlinear wave dynamics.
- extended Vakhnenko model,
- Khater Ⅲ technique,
- localized wave packets,
- nonlinear dispersive systems
Citation: Dan Chen. Nonlinear wave dynamics in dispersive media: analytical insights from the nonlinear modified generalized Vakhnenko equation[J]. AIMS Mathematics, 2025, 10(7): 16407-16413. doi: 10.3934/math.2025734

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Abstract

This investigation explores the nonlinear modified generalized Vakhnenko (NMGV) equation, a pivotal model of nonlinear wave interactions within nonlinear dispersive media. The equation represents an extension of the classical Vakhnenko framework, integrating higher-order nonlinearities that significantly impact wave propagation. Comprehending these effects is essential for propelling the advancement of nonlinear wave theory in mathematical physics and engineering contexts. Utilizing the Khater Ⅲ method, we derive exact solutions that encapsulate the salient features of the NMGV equation's wave configurations. The research unveils innovative soliton-like solutions, shedding light on the intricate nonlinear mechanisms at play. These findings underscore the efficacy of the proposed methodology in addressing intricate nonlinear systems and highlight its applicability to analogous nonlinear evolution equations. By introducing novel analytical solutions, this study enriches the comprehension of dispersive wave phenomena and offers valuable insights for future research in nonlinear wave dynamics.

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