Asymptotic Behavior for a Class of Solutions to the Critical Modified Zakharov-Kuznetsov Equation
نویسندگان
چکیده
منابع مشابه
Asymptotic Behavior for a Class of Solutions to the Critical Modified Zakharov-kuznetsov Equation
We consider the initial value problem (IVP) associated to the modified Zakharov-Kuznetsov (mZK) equation ut + 6uux + uxxx + uxyy = 0, (x, y) ∈ R, t ∈ R, which is known to have global solution for given data in u(x, y, 0) = u0(x, y) ∈ H(R) satisfying ‖u0‖L2 < √ 3‖φ‖L2 , where φ is a solitary wave solution. In this work, the issue of the asymptotic behavior of the solutions of the modified Zakhar...
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The modied Zakharov–Kuznetsov (mZK) equation, ut + uux + uxxx + uxyy = 0, (1) represents an anisotropic two-dimensional generalization of the Korteweg–de Vries equation and can be derived in a magnetized plasma for small amplitude Alfvén waves at a critical angle to the undisturbed magnetic field, and has been studied by many authors because of its importance [1–5]. However, Eq. (1) possesses m...
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ژورنال
عنوان ژورنال: Studies in Applied Mathematics
سال: 2010
ISSN: 0022-2526,1467-9590
DOI: 10.1111/j.1467-9590.2009.00469.x