The Improved(G’/G)-Expansion Method for the (2+1)-Dimensional Modified Zakharov-Kuznetsov Equation
نویسندگان
چکیده
منابع مشابه
The Improved (G'/G)-Expansion Method for the (2+1)-Dimensional Modified Zakharov-Kuznetsov Equation
we apply the improved G′/G -expansion method for constructing abundant new exact traveling wave solutions of the 2 1 -dimensional Modified Zakharov-Kuznetsov equation. In addition, G ′′ λG′ μG 0 together with b α ∑w q −w pq G ′/G q is employed in this method, where pq q 0,±1,±2, . . . ,±w , λ and μ are constants. Moreover, the obtained solutions including solitons and periodic solutions are des...
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We prove that the initial value problem for the two-dimensional modified ZakharovKuznetsov equation is locally well-posed for data in H(R), s > 3/4. Even though the critical space for this equation is L(R) we prove that well-posedness is not possible in such space. Global well-posedness and a sharp maximal function estimate are also established.
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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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متن کاملGeneralized and Improved (G′/G)-Expansion Method for (3+1)-Dimensional Modified KdV-Zakharov-Kuznetsev Equation
The generalized and improved (G'/G)-expansion method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. In this article, we investigate the higher dimensional nonlinear evolution equation, namely, the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation via this powerful method. The solutions...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics
سال: 2012
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2012/438928