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Multi-symplectic Methods for Some Nonlinear Wave Equations

Author: ChenYaMing
Tutor: SongSongHe
School: National University of Defense Science and Technology
Course: Mathematics
Keywords: Nonlinear wave equation Multisymplectic Conservation laws Camassa-Holm equation KdV equation Nonlinear Schr (o ¨) dinger equation Zakharov-Kuznetsov equation Kadomtsev-Petviashvili equation
CLC: O241.82
Type: Master's thesis
Year: 2010
Downloads: 77
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Abstract


Many important equations of mathematical physics can be expressed as multisymplectic Hamiltonian system form , which undoubtedly has a very important significance of their numerical algorithm . Multisymplectic geometry structure inherent geometric properties of this structure , which requires to be maintained in the numerical discretization multisymplectic Hamiltonian system , we are said to be able to maintain this discrete the multisymplectic geometric structure of the algorithm for the multi-symplectic algorithm . A large number of numerical results in Table the Ming Duoxin algorithm compared to the numerical simulation of long non multisymplectic algorithm has obvious advantages . In this paper, some important one-dimensional and two-dimensional nonlinear wave equations multisymplectic algorithm . The main findings are as follows: 1 , respectively construct Camassa-Holm equation multisymplectic Fourier spectrum discrete multisymplectic Fourier pseudospectral format KdV equation format multisymplectic Fourier pseudospectral format . In addition , we for the first time into the Ito -type coupled KdV equation the multisymplectic Hamilton in the form of partial differential equations and construct its multi- symplectic Fourier pseudospectral format . 2 , respectively, to construct the coupled nonlinear Schr ( o | ¨ ) dinger equation for two-dimensional nonlinear Schr ( o | ¨ ) dinger equation multisymplectic splitting scheme . 3 , to construct a the two Wei Duoxin Hamilton partial differential equations multi- symplectic Fourier pseudospectral format and the format of the corresponding discrete multi- symplectic conservation law , this algorithm is applied to solve the two-dimensional Zakharov-Kuznetsov equation and two-dimensional Kadomtsev - Petviashvili equation , these two equations are constructed multi- symplectic Fourier pseudospectral format . 4 algorithm constructed by the large number of numerical examples to verify its effectiveness and the superiority of the long-time numerical simulation .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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