Propagating Wave Patterns in a Derivative Nonlinear Schrödinger System with Quintic Nonlinearity

Abstract

Exact expressions are obtained for a diversity of propagating patterns for a derivative nonlinear Schrödinger equation with the quintic nonlinearity. These patterns include bright pulses, fronts and dark solitons. The evolution of the wave envelope is determined via a pair of integrals of motion, and reduction is achieved to Jacobi elliptic cn and dn function representations. Numerical simulations are performed to establish the existence of parameter ranges for stability. The derivative quintic nonlinear Schrödinger model equations investigated here are relevant in the analysis of strong optical signals propagating in spatial or temporal waveguides.

Carroll-type deformations in nonlinear elastodynamics

“…In order that the nonlinear potential (22) attains a minimum at the undeformed configuration, h 0 must be positive and either (a) h 1 0 and p > −1 or (b) h 1 < 0 and p > 0. Specializing the dispersion relation (19) for the nonlinear potential (22) yields…”

“…Taking into account (57), we substitute the velocity V = ω/k with V = V + mc/k in (71) in order to compare the dispersion relations ( 19) and (71). When the square of wave amplitude lies in an interval in which the potential F is decreasing, or dF d|ψ| 2 (A 2 ) is positive but small enough to satisfy (69), the dispersion relation (71) approximates (19) for waves whose wavelength is, in modulus, larger than m −1 (see figure 5).…”

“…This nonlinear equation is not integrable in general. However, it is of interest to seek integrable Hamiltonian subsystems, in particular, of the type recently considered in the context of resonant derivative NLS models in [18], quintic and nonic NLS equations in [7,19] and most recently of non-integrable coupled Manakov-type systems in [20].…”

“…An analogous procedure has recently been adopted in [19] to isolate gray solitary pulses in a quintic derivative NLS model.…”

Dynamical behavior and exact solution in invariant manifold for a septic derivative nonlinear Schrödinger equation

“…A procedure recently employed by [13][14][15][16] (the application of a pair of invariants of motion) is also applied here. where A 2 be the squared amplitude, x and t are the normalized spatial coordinate and retarded time, respectively.…”