Classical Lie symmetry analysis is proposed to get a new variety of similarity solutions nonlinear (3+1)-modified Korteweg de Vries-Zakharov–Kuznetsov equation. The equation often used control the type weakly ion-acoustic waves in homogeneous magnetised electron-positron plasma. In plasma, including some hot and cold ions, such exist. By comparing results reported earlier, analytical are create...

We prove local well-posedness for the L2 critical generalized Zakharov-Kuznetsov equation in Hs, s∈(3/4,1). also that is “almost well-posedness” initial data u0∈Hs, s∈[1,2), sense solution belongs to a certain intersection C([0,T]:Hs(R3))∩XTs and unique within class, where we can ensure continuity of data-to-solution map an only slightly larger space. solutions satisfy expected conservation L2−...

A variational method given by Ritz has been applied to the Zakharov equation to construct an analytical solution. The solution of Zakharov equation gives a good description of both linear and nonlinear evolutions of instabilities generated in waves due to modulation. The spatially periodic trial function is chosen in the form of combination of Jacobian elliptic functions with the dependence of ...

We consider in this paper the rigorous justification of the ZakharovKuznetsov equation from the Euler-Poisson system for uniformly magnetized plasmas. We first provide a proof of the local well-posedness of the Cauchy problem for the aforementioned system in dimensions two and three. Then we prove that the long-wave small-amplitude limit is described by the ZakharovKuznetsov equation. This is d...

Related Articles Comment on “On the consistency of the solutions of the space fractional Schrödinger equation” [J. Math. Phys. 53, 042105 (2012)] J. Math. Phys. 53, 084101 (2012) Rotating 2N-vortex solutions to the Gross-Pitaevskii equation on S2 J. Math. Phys. 53, 083701 (2012) Existence of attractors for modified Zakharov equations for plasmas with a quantum correction J. Math. Phys. 53, 0727...