In the long wave regime, nonlinear waves may undergo a phase transition from a smooth behavior to a fast oscillatory behavior. In this study, we consider this phenomenon, which is commonly known as dispersive shock, in the light of Dubrovin's universality conjecture (Dubrovin, 2006; Dubrovin and Elaeva, 2012) and we argue that the transition can be described by a special solution of a model universal partial differential equation. This universal solution is constructed using the string equation. We provide a classification of universality classes and an explicit description of the transition with special functions, thereby extending Dubrovin's universality conjecture to a wider class of equations. In particular, we show that the Benjamin-Ono equation belongs to a novel universality class with respect to those known previously, and we compute its string equation exactly. We describe our results using the language of statistical mechanics, where we show that dispersive shocks share many of the features of the tricritical point in statistical systems, and we also build a dictionary of the relations between nonlinear waves and statistical mechanics.

Masoero, D., Raimondo, A., Antunes, P. (2015). Critical behavior for scalar nonlinear waves. PHYSICA D-NONLINEAR PHENOMENA, 292-293, 1-7 [10.1016/j.physd.2014.09.007].

Critical behavior for scalar nonlinear waves

RAIMONDO, ANDREA
Secondo
;
2015

Abstract

In the long wave regime, nonlinear waves may undergo a phase transition from a smooth behavior to a fast oscillatory behavior. In this study, we consider this phenomenon, which is commonly known as dispersive shock, in the light of Dubrovin's universality conjecture (Dubrovin, 2006; Dubrovin and Elaeva, 2012) and we argue that the transition can be described by a special solution of a model universal partial differential equation. This universal solution is constructed using the string equation. We provide a classification of universality classes and an explicit description of the transition with special functions, thereby extending Dubrovin's universality conjecture to a wider class of equations. In particular, we show that the Benjamin-Ono equation belongs to a novel universality class with respect to those known previously, and we compute its string equation exactly. We describe our results using the language of statistical mechanics, where we show that dispersive shocks share many of the features of the tricritical point in statistical systems, and we also build a dictionary of the relations between nonlinear waves and statistical mechanics.
Articolo in rivista - Articolo scientifico
Benjamin-Ono equation; Dispersive shock; Korteweg-de Vries equation; Phase transition; String equation; Tricritical point;
Benjamin-Ono equation; Dispersive shock; Korteweg-de Vries equation; Phase transition; String equation; Tricritical point; Condensed Matter Physics; Statistical and Nonlinear Physics
English
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Masoero, D., Raimondo, A., Antunes, P. (2015). Critical behavior for scalar nonlinear waves. PHYSICA D-NONLINEAR PHENOMENA, 292-293, 1-7 [10.1016/j.physd.2014.09.007].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/62621
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