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Negative‐order modified KdV equations: multiple soliton and multiple singular soliton solutions
Author(s) -
Wazwaz AbdulMajid,
Xu GuiQiong
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3507
Subject(s) - korteweg–de vries equation , mathematics , soliton , order (exchange) , operator (biology) , recursion (computer science) , mathematical physics , mathematical analysis , work (physics) , nonlinear system , physics , quantum mechanics , biochemistry , chemistry , finance , repressor , algorithm , transcription factor , economics , gene
In this work, we develop the negative‐order modified Korteweg–de Vries (nMKdV) equation. By means of the recursion operator of the modified KdV equation, we derive negative order forms, one for the focusing branch and the other for the defocusing form. Using the Weiss–Tabor–Carnevale method and Kruskal's simplification, we prove the Painlevé integrability of the nMKdV equations. We derive multiple soliton solutions for the first form and multiple singular soliton solutions for the second form. Copyright © 2015 John Wiley & Sons, Ltd.