Symmetry analysis and conservation laws of a further modified 3D Zakharov-Kuznetsov equation
نویسندگان
چکیده
منابع مشابه
Conservation Laws and Exact Solutions of a Generalized Zakharov-Kuznetsov Equation
In this paper, we study a generalized Zakharov–Kuznetsov equation in three variables, which has applications in the nonlinear development of ion-acoustic waves in a magnetized plasma. Conservation laws for this equation are constructed for the first time by using the new conservation theorem of Ibragimov. Furthermore, new exact solutions are obtained by employing the Lie symmetry method along w...
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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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We prove the local well-posedness of the three-dimensional Zakharov-Kuznetsov equation ∂tu+∆∂xu+u∂xu = 0 in the Sobolev spaces Hs(R3), s > 1, as well as in the Besov space B 2 (R 3). The proof is based on a sharp maximal function estimate in time-weighted spaces.
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In this paper, we study and classify the conservation laws of the ZakharovKuznetsov equations. It is shown that these can be obtained by studying the interplay between symmetry generators and ‘multipliers’. This is, particularly, useful for the higher-order multipliers. As a final note, we include Drinfeld-Sokolov-Wilson system to demonstrate the usefulness of the approach to systems of pdes. K...
متن کاملWell-posedness for the 2d Modified Zakharov-kuznetsov Equation
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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ژورنال
عنوان ژورنال: Results in Physics
سال: 2020
ISSN: 2211-3797
DOI: 10.1016/j.rinp.2020.103401