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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.5

ISSN Print: 2152-5102
ISSN Online: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v43.i5-6.20
pages 377-389

A Modified KdV Model of Waves with Evaporation from the Phase Surface

Liudmila Uvarova
Moscow State University of Technology "STANKIN"
Evgenii I. Galakhov
Department of Mathematics, Peoples' Friendship University Moscow, Russia
Ol'ga A. Salieva
Department of Applied Mathematics, Moscow State of Technology STANKIN Vadkovskii lane 3a, Moscow, 127055, Russia

ABSTRACT

In this paper we consider the impact of evaporation on formation of a gravitational wave in a potential approximation and study the condition of its existence in the form of a soliton. We study a nonlinear modified KdV equation, which takes into account the impact of a molecular mechanism (evaporation) at the dividing boundary "wave front − environment" on wave propagation. A nonlinear analysis is given. It is shown that, in general, modification of the KdV equation by introducing an additional stochastic term determined by a certain physical or physico-chemical process gives rise to solutions that are not Jacobi functions.