Abstract The nonlinear equation is obtained describing the dynamics of wave structures in dusty plasma above illuminated surface Moon case low frequencies and pancake-like shape packet direction along external magnetic field. This modified Zakharov – Kuznetsov equation. analytical formula for one-dimensional soliton solution derived. analysis stability was performed.

The Cauchy problem for the classical Dirac-Klein-Gordon system in two space dimensions is globally well-posed for L Schrödinger data and wave data in H 1 2 ×H − 1 2 . In the case of smooth data there exists a global smooth (classical) solution. The proof uses function spaces of Bourgain type based on Besov spaces – previously applied by Colliander, Kenig and Staffilani for generalized Benjamin-...

We analytically study the long time and large space asymptotics of a new broad class solutions KdV equation introduced by Dyachenko, Zakharov, Zakharov. These are characterized Riemann--Hilbert problem which we show arises as limit $N\to \infty$ gas $N$-solitons. that this solitons in $N \to is slowly approaching cnoidal wave solution for $x - (up to terms order $\mathcal{O} (1/x)$), while zero...

Using a traveling wave reduction technique, we have shown that Maccari equation, (2?1)-dimensional nonlinear Schrödinger equation, medium equal width equation, (3?1)-dimensional modified KdV–Zakharov– Kuznetsev equation, (2?1)-dimensional long wave-short wave resonance interaction equation, perturbed nonlinear Schrödinger equation can be reduced to the same family of auxiliary elliptic-like equ...