6533b852fe1ef96bd12aa4ff

RESEARCH PRODUCT

Generalized Camassa-Holm Equations: Symmetry, Conservation Laws and Regular Pulse and Front Solutions

Maria Luz GandariasMaría S. BruzónGaetana Gambino

subject

Holm equationsIntegrable systemGeneral MathematicsInfinitesimalNonclassical symmetries01 natural sciencesdouble reduction010305 fluids & plasmas0103 physical sciencesmultiplier methodComputer Science (miscellaneous)QA1-939Generalized Camassa–Holm equationsHomoclinic orbit010306 general physicsEngineering (miscellaneous)Settore MAT/07 - Fisica MatematicaConvergent seriesmulti-infinite series solutionsMathematicsMathematical physicsConservation lawsnonclassical symmetriesConservation lawHomoclinic and heteroclinic orbitsMulti-infinite series solutionsDouble reductionSymmetry (physics)Pulse (physics)generalized Camassa&#8211Mathematics::LogicMultiplier methodHomogeneous spaceconservation lawshomoclinic and heteroclinic orbitsMathematics

description

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.

yearjournalcountryeditionlanguage
2021-04-01
10.3390/math9091009http://hdl.handle.net/10498/24992