TY - JOUR

T1 - Snake Solitons in the Cubic-Quintic Ginzburg-Landau Equation

AU - Mancas, S.C.

AU - Choudhury, Roy S.

AU - Mancas, Stefani

N1 - Comprehensive numerical simulations of pulse solutions of the cubic-quintic Ginzburg-Landau equation (CGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz.

PY - 2009/9

Y1 - 2009/9

N2 - Comprehensive numerical simulations of pulse solutions of the cubic–quintic Ginzburg–Landau equation (CGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons. In contrast to the regular solitary waves investigated in numerous integrable and non-integrable systems over the last three decades, these dissipative solitons [ C.I. Christov, M.G. Velarde, Dissipative solitons, Physica D 86 (1995) 323 ] are not stationary in time. Rather, they are spatially confined pulse-type structures whose envelopes exhibit complicated temporal dynamics. The numerical simulations also reveal very interesting bifurcations sequences of these pulses as the parameters of the CGLE are varied.

AB - Comprehensive numerical simulations of pulse solutions of the cubic–quintic Ginzburg–Landau equation (CGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons. In contrast to the regular solitary waves investigated in numerous integrable and non-integrable systems over the last three decades, these dissipative solitons [ C.I. Christov, M.G. Velarde, Dissipative solitons, Physica D 86 (1995) 323 ] are not stationary in time. Rather, they are spatially confined pulse-type structures whose envelopes exhibit complicated temporal dynamics. The numerical simulations also reveal very interesting bifurcations sequences of these pulses as the parameters of the CGLE are varied.

UR - https://www.sciencedirect.com/science/article/pii/S0378475409001803

U2 - 10.1016/j.matcom.2009.06.017

DO - 10.1016/j.matcom.2009.06.017

M3 - Article

VL - 80

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

ER -