Conservative compact difference schemes for the coupled nonlinear schrödinger system. Issue 3 (20th December 2013)

• Record Type: Journal Article
• Authors: Hu, Xiuling; Zhang, Luming
• Is Part Of: Numerical methods for partial differential equations. Volume 30:Issue 3(2014:May)
• Page Start: 749
• Page End: 772
• Publication Date: 2013-12-20
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21826
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>In this article, some conservative compact difference schemes are explored for the strongly coupled nonlinear schrödinger system. After transforming the scheme into matrix form, we prove the existence and uniqueness, convergence and stability of the difference solutions for one nonlinear scheme in the <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg4vp2jdw9" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:0749159X:media:num21826:num21826-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mrow></mml:math></alternatives> norm by using some techniques of matrix theory. Numerical results show that one nonlinear scheme is the most efficient of all the compact schemes constructed here. It allows much larger time steps than the others. The second most efficient compact scheme is a linear one. We then give numerical simulations to two soliton interactions for the two most efficient compact schemes. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 749–772, 2014</p> </abstract>