Abstract The main purpose here is the study of dispersive blow-up for solutions Zakharov-Kuznetsov equation. Dispersive refers to point singularities due focusing short or long waves. We will construct initial data such that linear problem present this kind singularities. Then we show corresponding nonlinear inherited from component part Similar results are obtained generalized

In this paper,the traditional G′/G-expansion method is improved and a generalized G′/G-expansion method is proposed to seek exact solutions of nonlinear evolution equations.And we choose Benjamin-Bona-Mahony equation,(2+1) dimensional generalized Zakharov-Kuznetsov equation and variant Bousinessq equations to illustrate the validity and advantages of the proposed method.It is shown that the pro...

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.

Further extension of the generalized and improved (G0/G)-expansion method; Nonlinear ordinary differential equation; ZKBBM equation; Travelling wave solutions Abstract In this article, the generalized and improved (G0/G)-expansion method has been proposed for further extension to generate many new travelling wave solutions. In addition, nonlinear ordinary differential equation is implemented as...

We provide a treatment of algebro-geometric solutions of the classical massive Thirring system in the framework of the Weierstrass–Klein theory of hyperelliptic functions. We show that the equations of this model generate the characteristic relations of hyperelliptic theory of even hyperelliptic curves, the same role that the KdV equation plays for odd hyperelliptic curves. We also consider the...

Transverse instabilities correspond to a class of perturbations traveling in a direction transverse to the direction of the basic solitary wave. Solitary waves traveling in one space direction generally come in one-parameter families. We embed them in a two-parameter family and deduce a new geometric condition for transverse instability of solitary waves. This condition is universal in the sens...