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Multi- branch Ermakov equation

Author: ZuoZuo
Tutor: QuChangZheng
School: Northwestern University
Course: Applied Mathematics
Keywords: Multibranched Ermakov system : L-R-R invariants Hamiltonian structure Superposition principle Geometric integrability Nonlocal symmetry
CLC: O175.2
Type: Master's thesis
Year: 2011
Downloads: 9
Quote: 0
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Abstract


Recent decades , discussions of Ermakov system has been important achievements Ermakov system is a pair of mutually coupled second-order differential equations , it has similar properties and Pinney equation , harmonic oscillator equations with time variable . Mainly is characterized by the nature of the time integral can be obtained according to this nature the Ermakov systems allow LRR (Lewis-Ray-Reid) invariants . this invariant in the process of research Ermakov system plays an important role , can be used to construct non- linear superposition theorem and linear systems . particular, we are given three branches and four branch Ermakov system allows the LRR invariant and the nonlinear superposition theorem In this paper, multi- branch Ermakov system is mainly divided into three parts the first part is from Pinney equation and branch Ermakov system determine the Lie symmetry group of Lie symmetry group identified by the group of canonical coordinates or differential invariants obtained equation invariant second part of the second branch of the Ermakov system Ermakov system . promotion to the multi- branch and thus the two branch Ermakov system LRR invariant extended to multi- branch Ermakov system allows LRR invariant . third part focuses on the principle of superposition of multi- branch Ermakov system . research ideas : a order differential equations of the superposition principle , the promotion to the second-order differential equations , the Ermakov system which leads to the superposition principle . earlier has two branch Ermakov system to promote Ermakov system to a multi- branch , here we mainly discuss multi-branch the Ermakov system also meet superimposed the principle of the fourth part of the multi- branch system of geometric Camassa-Holm and Hunter-Saxton integrability chapter introduces the multi-branch Camassa-Holm and Hunter-Saxton system , given the multi-branch Camassa-Holm, Hunter-Saxton and μ -Camassa-Holm the system geometry integrable , said they intended for the spherical surfaces , you can direct the construction of their conservation laws of infinite number .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations
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