Multi-symplectic Scheme and Norm Conserving Law of Generalized Nonlinear Schrödinger Equation

CHINESE JOURNAL OF COMPUTATIONAL PHYSICS ›› 2009, Vol. 26 ›› Issue (5): 693-698.

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Multi-symplectic Scheme and Norm Conserving Law of Generalized Nonlinear Schrödinger Equation

HUANG Langyang

School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

Received:2007-10-15 Revised:2008-05-07 Online:2009-09-25 Published:2009-09-25

Abstract

Abstract: Multi-symplectic system for generalized nonlinear Schrödinger equation is constructed by canonical transformation.A new norm conserving multi-symplectic scheme is derived.Numerical experiments show that the multi-symplectic scheme shows excellent long-time numerical behavior and preserves norm conserving law better than both leap-frog scheme and symplectic Euler middle scheme.

Key words: generalized nonlinear Schrödinger equation, multi-symplectic system, conservation law, multi-symplectic scheme, numerical experiments

CLC Number:

O241.82

HUANG Langyang. Multi-symplectic Scheme and Norm Conserving Law of Generalized Nonlinear Schrödinger Equation[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 26(5): 693-698.

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Multi-symplectic Scheme and Norm Conserving Law of Generalized Nonlinear Schrödinger Equation

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