THE MODIFIED WHITHAM MODULATION THEORY FOR THE NONLINEAR KLEIN-GORDON-FOCK EQUATION WITH THE SIMPLEST RATIONAL FUNCTION AS ITS POTENTIAL

Autor:	E.S. Alekseeva, A.E. Rassadin
Rok vydání:	2019
Předmět:	Physics Nonlinear system symbols.namesake Work (thermodynamics) Amplitude symbols Interval (mathematics) Rational function Klein–Gordon equation Stable distribution Mathematical physics Fock space
Zdroj:	The XXII workshop of the Council of nonlinear dynamics of the Russian Academy of Sciences. 47:12-14
ISSN:	2587-9634 1564-2291
DOI:	10.29006/1564-2291.jor-2019.47(1).2
Popis:	It is well-known that one can construct approximate solution of the nonlinear KleinGordon-Fock equation (NKGF) by means of the Whitham modulation theory (Whitham, 1977). In this work in the framework of the modified Whitham modulation theory presented at (Alekseeva, Rassadin, 2018) and (Kostromina et al., 2017) for NKGF with potential U(x) = (x–1/x)2 its asymptotic solution v(x, t) has been found. Due to isochronism of onedimensional movement of classical particle with unit mass in this potential amplitude a(x, t) of asymptotical solution obeys the linear transfer equation ∂a/∂t + V∂a/∂x = 0 with velocity V belonging to the interval –1 of asymptotic solution of NKGF has been calculated under assumption that its initial phase shift is random value with stable distribution of probabilities. The obtained asymptotic solution due to its simplicity and informativity can be used by lecturers to illustrate abilities of the Whitham modulation theory.
Databáze:	OpenAIRE
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