soliton and similarity solutions of ν = 2, 4 supersymmetric equations孤子和相似性解ν= 2,4超对称方程.pdf

Symmetry 2012, 4, 441-451; doi:10.3390/sym4030441 OPEN ACCESS symmetry ISSN 2073-8994 /journal/symmetry Article Soliton and Similarity Solutions of N , Supersymmetric Equations , ´ , Laurent Delisle * and Veronique Hussin ´ ´ ´ ´ Departement de Mathematiques et de Statistique, Universite de Montreal, C.P. 6128, Succursale ´ Centre-ville, Montreal, (QC) H3C 3J7, Canada; E-Mail: hussin@dms.umontreal.ca ´ ´ ´ Centre de Recherches Mathematiques, Universite de Montreal, C.P. 6128, Succursale Centre-ville, ´ ´ Montreal (Quebec) H3C 3J7, Canada * Author to whom correspondence should be addressed; E-Mail: delisle@dms.umontreal.ca; Tel.: +1-514-343-6743; Fax:+1-514-343-5700. Received: 25 May 2012 / Accepted: 27 July 2012 / Published: 8 August 2012 Abstract: We produce soliton and similarity solutions of supersymmetric extensions of Burgers, Korteweg–de Vries and modified KdV equations. We give new representations of the τ -functions in Hirota bilinear formalism. Chiral superfields are used to obtain such solutions. We also introduce new solitons called virtual solitons whose nonlinear interactions produce no phase shifts. Keywords: supersymmetric equations; solitons; Hirota bilinear formalism Classification: MSC 35Q51, 35Q53, 81Q60 1. Introduction The study of N supersymmetric (SUSY) extensions of nonlinear evolution equations has been largely studie