Geodesic
Convective Modulation Instability of the Radiation of the Periodic Component in the Case of Resonance of Long and Short Waves
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern Methods of Mechanics, Tome 322 (2023), pp. 124-132

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The main result of the paper is a theorem stating that the modulation instability of a carrier periodic wave of small (but finite) amplitude propagating in an arbitrary dispersive medium may only be convective in a reference frame moving at a velocity that differs finitely from the group velocity of this wave. The application of this result to the radiation of a resonant wave by a soliton-like “core” is discussed. Such radiation occurs in media where classical solitary waves are replaced with generalized solitary waves as a result of linear resonance of long and short waves. Generalized solitary waves are traveling waves that form a homoclinic structure doubly asymptotic to a periodic wave.
Keywords: radiation of a resonant wave, convective modulation instability, central manifold, reduced system of equations, generalized solitary wave. 
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     author = {A. T. Il'ichev},
     title = {Convective {Modulation} {Instability} of the {Radiation} of the {Periodic} {Component} in the {Case} of {Resonance} of {Long} and {Short} {Waves}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {124--132},
     publisher = {mathdoc},
     volume = {322},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/TM_2023_322_a9/}
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A. T. Il'ichev. Convective Modulation Instability of the Radiation of the Periodic Component in the Case of Resonance of Long and Short Waves. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern Methods of Mechanics, Tome 322 (2023), pp. 124-132. http://geodesic.mathdoc.fr/item/TM_2023_322_a9/