The overtaking collisional phenomenon of slow shear Alfvén solitons are studied in a low beta (β = kinetic pressure/magnetic pressure) collisionless, magnetized plasma consisting electron and ion fluids. By employing reductive perturbation technique, the Korteweg–de Vries (KdV) equation is deduced for investigating nonlinear wave. Before embarking on study collisions, stability analysis KdV usi...

Complete discrimination system for polynomial and direct integral method were discussed systematically. In particularly, we pointed out some mistaken viewpoints. Combining with complete discrimination system for polynomial, direct integral method was developed to become a powerful method and was applied to a lot of nonlinear mathematical physics equations. All single traveling wave solutions to...

Bu çalışmada, Drinfeld–Sokolov–Satsuma–Hirota (DSSH) denkleminin yaklaşık çözümü rezidual kuvvet seri metodu (RKSM) kullanılarak elde edildi. Kesirli türevleri karakterize etmek için uyumlu türev yaklaşımı kullanıldı ve farklı operatör değerleri RKSM çözümleri kesin çözümlerle çeşitli tablo grafikler karşılaştırıldı. Sonuçlar; uygulanan tekniğin kullanımının kolay, çok başarılı tutarlı olduğunu...

Under investigation in this work is the coupled Sasa-Satsuma equation, which can describe propagations of two optical pulse envelopes birefringent fibers. The Riemann-Hilbert problem for equation formulated on basis corresponding $5 \times 5$ matrix spectral problem, allows us to present a suitable representation solution equation. Then Deift-Zhou steepest descent method used analyze long time ...

We study the stability of spatially periodic solutions to the Kawahara equation, a fifth order, nonlinear partial differential equation. The equation models the propagation of nonlinear water-waves in the long-wavelength regime, for Weber numbers close to 1/3 where the approximate description through the Korteweg-de Vries (KdV) equation breaks down. Beyond threshold, Weber number larger than 1/...

In this paper, we discuss the Hamiltonian structure of Korteweg–de Vries equation, modified Korteweg–de Vries equation, and generalized Korteweg– de Vries equation. We proposed the Sine-function algorithm to obtain the exact solution for non-linear partial differential equations. This method is used to obtain the exact solutions for KdV, mKdV and GKdV equations. Also, we have applied the method...