EXACT SOLUTIONS OF GENERALIZED NONLINEAR VAKHNENKO-PARKES EQUATION
https://doi.org/10.26583/vestnik.2025.3.4
EDN: NFYDTS
Abstract
In this paper, one of generalized Vakhnenko-Parkes’ family equations is considered describing the propagation of short-wave disturbances in relaxing media, taking into account the dependence of the wave velocity on the amplitude. A general quadrature solution is obtained for the equation under consideration by reducing it to an ordinary differential equation using traveling wave variables. Some formal exact solutions of the initial equation are found. Periodic exact solutions are expressed in terms of Jacobi elliptic functions. An explicit solution is also presented, expressed in terms of a power function of spatial and temporal variables. The obtained exact solutions can be used as test functions when analyzing the results of numerical simulation of processes in relaxing medium described by Vakhnenko-Parkes type equations.
Keywords
Vakhnenko-Parkes equation,
exact solutions,
solutions in quadratures,
solutions in traveling wave variables,
Jacobi elliptic functions
Supporting agencies: The work was supported by the Ministry of Science and Higher Education of the Russian Federation (state assignment project No. FSWU-2023-0031)
About the Authors
K. M. Zuev
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
N. A. Kudryashov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
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Review
For citations:
Zuev K.M., Kudryashov N.A. EXACT SOLUTIONS OF GENERALIZED NONLINEAR VAKHNENKO-PARKES EQUATION. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2025;14(3):214-224. (In Russ.) https://doi.org/10.26583/vestnik.2025.3.4. EDN: NFYDTS
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