Generalized Camassa–Holm equations: Symmetry, conservation laws and regular pulse and front solutions

Gaetana Gambino, Maria Santos Bruzón, Maria Luz Gandarias

Risultato della ricerca: Articlepeer review

Abstract

In this paper, we consider a member of an integrable family of generalized Camassa–Holm (GCH) equations. We make an analysis of the point Lie symmetries of these equations by using the Lie method of infinitesimals. We derive nonclassical symmetries and we find new symmetries via the nonclassical method, which cannot be obtained by Lie symmetry method. We employ the multiplier method to construct conservation laws for this family of GCH equations. Using the conservation laws of the underlying equation, double reduction is also constructed. Finally, we investigate traveling waves of the GCH equations. We derive convergent series solutions both for the homoclinic and heteroclinic orbits of the traveling-wave equations, which correspond to pulse and front solutions of the original GCH equations, respectively.
Lingua originaleEnglish
pagine (da-a)1-20
Numero di pagine20
RivistaMathematics
Volume9
Stato di pubblicazionePublished - 2021

All Science Journal Classification (ASJC) codes

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