Singularity analysis and integrability for a HNLS equation governing pulse propagation in a generic fiber optics

Symbolic computation on the Darboux transformation for a generalized variable-coefficient higher-order nonlinear Schrödinger equation from fiber optics

“…, (24) from which, we know that a series of analytic solutions including the soliton-like solutions for Eq. (1) under constraints (5) can be derived by solving the linear eigenvalue problem (6) with an initial potential and performing tedious but not complicated algebraic operations [37][38][39].…”

“…The authors in Ref. [24] have investigated Eq. (1) by the Painlevé analysis method [32] and obtained the following integrable constraint conditions,…”

“…With this constraint conditions, a Lax pair (also called zero-curvature representation) for Eq. (1) has been presented in the 3 × 3 matrix form [24]. However, it is found that the entries of the principal diagonal in the 'time' part of the Lax pair are the same parameters, which implies that this linear eigenvalue problem is not suitable for constructing the Darboux transformation.…”

Bäcklund transformation and conservation laws for the variable-coefficient N-coupled nonlinear Schrödinger equations with symbolic computation

“…Regarding the inhomogeneous media and nonuniform boundary in the realistic situations, the variable-coefficient NLEEs have currently been one of the research hotpoints [5,6]. In this paper, considering the inhomogeneous effects such as the variational loss rate and time-dependent chirping/phase modulation in the optical fibers or nonconstant damping and time-dependent linear and parabolic density profiles in plasmas, we will investigate the variable-coefficient N -coupled nonlinear Schrödinger equations written as N) represent the simultaneous wave propagation of N fields in the optical fibers and plasmas, and α(t), β(t) and γ(t) are real analytical functions and the prime denotes the derivative with respect to t. Eqs.…”

A modified Calogero-Bogoyavlenskii-Schiff equation with variable coefficients and its non-isospectral Lax pair

“…Therefore, equations with variable coefficients may provide various models for real physical phenomena, for example, in the propagation of small-amplitude surface waves, which run on straits or large channels of slowly varying depth and width. On one hand, the variable-coefficient generalizations of nonlinear integrable equations are a currently exciting subject [19][20][21][22] (and also [21,]). Many researchers have mainly investigated (1 + 1) dimensional nonlinear integrable systems with constant coefficients for discovery of new nonlinear integrable systems.…”