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Asymptotic Behavior for a Class of Solutions to the Critical Modified Zakharov–Kuznetsov Equation
Author(s) -
Panthee M.,
Scialom M.
Publication year - 2010
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2009.00469.x
Subject(s) - mathematics , class (philosophy) , scaling , work (physics) , energy method , mathematical physics , mathematical analysis , physics , computer science , thermodynamics , geometry , artificial intelligence
We consider the initial value problem (IVP) associated to the modified Zakharov–Kuznetsov (mZK) equationwhich is known to have global solution for given data in satisfying , where φ is a solitary wave solution. In this work, the issue of the asymptotic behavior of the solutions of the modified Zakharov–Kuznetsov equation with negative energy is addressed. The principal tool to obtain the main result is the use of appropriate scaling argument from Angulo et al. [1, 2].