46 citations · 342 across the 43 of their papers we have counts for
9 papers · 1 filter
Dissipative periodic and chaotic patterns to the KdV--Burgers and Gardner equations
Stefan C. Mancas, Ronald Adams
We investigate the KdV-Burgers and Gardner equations with dissipation and external perturbation terms by the approach of dynamical systems and Shil'nikov's analysis. The stability…
Traveling Wave Solutions to Fifth- and Seventh-order Korteweg-de Vries Equations: Sech and Cn Solutions
Stefan C. Mancas, Willy A. Hereman
In this paper we review the physical relevance of a Korteweg-de Vries (KdV) equation with higher-order dispersion terms which is used in the applied sciences and engineering. We al…
Traveling wave solutions to Kawahara and related equations
Stefan C. Mancas
Traveling wave solutions to Kawahara equation (KE), transmission line (TL), and Korteweg-de Vries (KdV) equation are found by using an elliptic function method which is more genera…
Numerical Simulations of Snake Dissipative Solitons in Complex Cubic-Quintic Ginzburg-Landau Equation
Stefan C. Mancas, Harihar Khanal
Numerical simulations of the complex cubic-quintic Ginzburg-Landau equation (CCQGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide…
Weierstrass traveling wave solutions for dissipative BBM equation
Stefan C. Mancas, Greg Spradlin, Harihar Khanal
In this paper the effect of a small dissipation on waves is included to find exact solutions to the modified BBM equation. Using Lyapunov functions and dynamical systems theory, we…
Spatiotemporal two-dimensional solitons in the complex Ginzburg-Landau equation
Florent Bérard, Stefan C. Mancas
We introduce spatiotemporal solitons of the two-dimensional complex Ginzburg-Landau equation (2D CCQGLE) with cubic and quintic nonlinearities in which asymmetry between space-time…