TY - JOUR
T1 - Numerical Simulations of Snake Dissipative Solitons in Complex Cubic-Quintic Ginzburg-Landau Equation
AU - Mancas, S.C.
AU - Khanal, Harihar
AU - Mancas, Stefani
PY - 2009/4
Y1 - 2009/4
N2 - 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 variety of disciplines, reveal five entirely novel classes of pulse or solitary waves solutions, viz. pulsating, creeping, snaking, erupting, and chaotical solitons [9]. Here, we develop a theoretical framework for analyzing the full spatio-temporal structure of one class of dissipative solution (snaking soliton) of the CCQGLE using the variational approximation technique and the dynamical systems theory. The qualitative behavior of the snaking soliton is investigated using the numerical simulations of (a) the full nonlinear complex partial differential equation and (b) a system of three ordinary differential equations resulting from the variational approximation.
AB - 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 variety of disciplines, reveal five entirely novel classes of pulse or solitary waves solutions, viz. pulsating, creeping, snaking, erupting, and chaotical solitons [9]. Here, we develop a theoretical framework for analyzing the full spatio-temporal structure of one class of dissipative solution (snaking soliton) of the CCQGLE using the variational approximation technique and the dynamical systems theory. The qualitative behavior of the snaking soliton is investigated using the numerical simulations of (a) the full nonlinear complex partial differential equation and (b) a system of three ordinary differential equations resulting from the variational approximation.
UR - https://commons.erau.edu/cgi/viewcontent.cgi?article=1798context=publication
U2 - 10.48550/arXiv.1305.1192
DO - 10.48550/arXiv.1305.1192
M3 - Article
VL - 5
JO - Advances and Applications in Fluid Dynamics
JF - Advances and Applications in Fluid Dynamics
ER -