Related papers: Nonlinear Schr\"odinger Equation: Generalized Darb…
We construct breather and rogue wave solutions of a variable coefficient nonlinear Schr\"odinger equation with an external linear potential. This generalized model describes the nonlinear wave propagation in an inhomogeneous plasma/medium.…
We study a deformation of the nonlinear Schr\"odinger equation recently derived in the context of deformation of hierarchies of integrable systems. This systematic method also led to known integrable equations such as the Camassa-Holm…
Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1)-dimensional inhomogeneous nonlinear Schrodinger (NLS) equation with variable coefficients and parabolic potential to the…
In the present work, we explore the possibility of developing rogue waves as exact solutions of some nonlinear dispersive equations, such as the nonlinear Schr\"odinger equation, but also, in a similar vein, the Hirota, Davey-Stewartson,…
A method is presented to obtain the change in the potential and in the relevant wavefunction of a linear system of ordinary differential equations containing a spectral parameter, when that linear system is perturbed and a finite number of…
NonlinearSchrodinger.jl is a Julia package with a simple interface for studying solutions of nonlinear Schr\"odinger equations (NLSEs). In approximately ten lines of code, one can perform a simulation of the cubic NLSE using one of 32…
The derivative nonlinear Schrodinger (DNLS) equation is the canonical model for dynamics of nonlinear waves in plasma physics and optics. We study exact solutions describing rogue waves on the background of periodic standing waves in the…
Algebraic Bargmann and Darboux transformations for equations of a more general form than the Schr\"odinger ones with an additional functional dependence h(r) in the right-hand side of equations are constructed. The suggested generalized…
This paper constructs the $N$-fold Darboux transformation (DT) for the vector complex modified Korteweg-de Vries (vcmKdV) equation and presents its determinant representation. Utilizing the DT and multi-fold eigenvalue degeneracy, we derive…
General rogue waves are derived for the generalized derivative nonlinear Schrodinger (GDNLS) equations by a bilinear Kadomtsev-Petviashvili (KP) reduction method. These GDNLS equations contain the Kaup-Newell equation, the Chen-Lee-Liu…
We construct the multi-breather solutions of the focusing nonlinear Schr\"odinger equation (NLSE) on the background of elliptic functions by the Darboux transformation, and express them in terms of the determinant of theta functions. The…
We explore the form of rogue wave solutions in a select set of case examples of nonlinear Schr\"odinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe…
The double-periodic solutions of the focusing nonlinear Schrodinger equation have been previously obtained by the method of separation of variables. We construct these solutions by using an algebraic method with two eigenvalues.…
A generalization of the classical one-dimensional Darboux transformation to arbitrary n-dimensional oriented Riemannian manifolds is constructed using an intrinsic formulation based on the properties of twisted Hodge Laplacians. The…
The nonlocal Darboux transformation for the stationary axially symmetric Schr\"odinger and Helmholtz equations is considered. Formulae for the nonlocal Darboux transformation are obtained and its relation to the generalized Moutard…
The second-type derivative nonlinear Schr\"odinger (DNLSII) equation was introduced as an integrable model in 1979. Very recently, the DNLSII equation has been shown by an experiment to be a model of the evolution of optical pulses…
We investigate the nonisospectral effects of a semi-discrete nonlinear Schr\"{o}dinger equation, which is a direct integrable discretisation of its continuous counterpart. Bilinear form and double casoratian solution of the equation are…
We study discrete rogue waves in an array of nonlinear waveguides. We show that very small degree of disorder due to experimental imperfection has a deep effect on the formation of discrete rogue waves. We predict long-living discrete rogue…
Rogue waves on the periodic background are considered for the nonlinear Schrodinger (NLS) equation in the focusing case. The two periodic wave solutions are expressed by the Jacobian elliptic functions dn and cn. Both periodic waves are…
In this note, we generalize the nonlinearity-recovery result in [7] for classical cubic nonlinear Schr\"odinger equations to higher-order Schr\"odinger equations with a more general nonlinearity. More precisely, we consider a…