Dynamics of Jacobi elliptic and soliton solutions for the modified quadratic-cubic nonlinear Schrödinger equation

Controlled self-similar matter waves in PT-symmetric waveguide

“…( 6). This equation is considered in the work of Pal et al [19] to obtain a wide class of localized solutions under different parametric constraints. For all these localized solutions of Eq.…”

“…In order to make the paper self-contained, we sketch the essential steps of Ref. [19]. We consider the following form of travelling wave solution for Eq.…”

“…= 0, η = 0, δ = 0 , the Eq. ( 15) have rational dark soliton solution expressed as [19] ρ(ξ) = p q + sech(rξ) , with the conditions given as…”

“…Experimental work has been done to show the existence of bright solitons for attractive interactions (a < 0) [7] and dark solitons for repulsive interactions (a > 0) [8]. Authors have also studied the dynamics of BEC in the presence of competing cubic-quintic nonlinearity [9,10,11,12,13,14,15] and quadratic-cubic nonlinearity [16,17,18,19,20]. Over the past several years, there is a considerable interest on the existence of matter wave solutions for GP equation with time-dependent coefficients or generalized nonlinear Schrödinger equation (GNLSE) [21,22,23,24,25].…”

Chirped nonlinear resonant states in femtosecond fiber optics

“…We know that the cubic nonlinear Schrödinger equation (NLSE) or Gross-Pitaevskii eqution (GPE) with appropriate trapping potential aptly describes the dynamics of dilute-gas Bose-Einstein condensate (BEC) [17]. The fact that different traps used to arrest BEC has paved the way for finding new solutions of NLSE or GPE with new potentials [18][19][20][21][22][23][24]. We emphasize here that, our motivation to consider these resonant states in the presence of 'smart' potentials essentially, stems from this fact.…”