Pattern selection and modulational instability in the one-dimensional modified complex Ginzburg–Landau equation

On nonstandard chemotactic dynamics with logistic growth induced by a modified complex Ginzburg–Landau equation

“…denotes the quantum potential stemming from Bohmian mechanics. Equation ( 2) is commonly referred to as the modified complex Ginzburg-Landau equation [4][5][6][7][8][9] and has been revealed as a powerful tool in the modeling of collective motion in a superfluid background when considering vacuum dissipative effects, among other diffusive processes in nonequilibrium systems. [10][11][12] In a recent work, 13 the author showed the accurate connection between a nonlinear Schrödinger-Doebner-Goldin equation [14][15][16] with focusing cubic interaction, namely,…”

“…In a biomechanical context, 𝑛 and 𝑆 represent the cell and chemical concentrations, respectively. The link between the Schrödinger model ( 4) and the macroscopic system (5) was established through the hydrodynamic laws governing the time evolution of the modulus square (𝑛 = |𝜓| 2 ) and the argument (𝑆 = 𝑖 2 log(𝜓∕𝜓))…”

New explicit and exact traveling waves solutions to the modified complex Ginzburg Landau equation

“…Among these studies of soliton-like solutions which propagated by conserving its velocity and shaped, several studies have been conducted on the modified Complex Ginzburg Landau Equation (CGLE) [15][16][17][18], [22].…”

Temporal Solitons in Nonlinear Media Modeled by Modified Complex Ginzburg Landau Equation Under Collective Variable Approach

“…They obtain explicit expressions for fixed amplitude, arbitrary amplitude and chirp free solutions. In a different study, Mohamadau et al [32] have studied the modulation instability in the 1D MCGLE with the complex nature of all the system parameters p, q, c, d, γ and obtained the contribution of the modified terms in the well known Lange and Newell's criteria. Recently, using the method of paraxial ray approximation, Hong [33] has reported the existence of a family of stationary solitons in a system modeled by real values of p, q, c, d and purely imaginary γ .…”