Search

In this study, we present the rigorous theory of the robust inverse scattering method for the discrete high-order nonlinear Schrödinger (HNLS) equation with a nonzero boundary condition (NZBC). Using the direct scattering problem, we deduce the analyticity, symmetries, and asymptotic behaviors of the Jost solutions and scattering matrix. We also formulate the inverse scattering problem using the matrix Riemann–Hilbert problem (RHP). Furthermore, utilizing the loop group theory, we construct the multi-fold Darboux transformation (DT) within the framework of the robust inverse scattering transform. Additionally, we develop the corresponding Bäcklund transformation (BT) to obtain the multi-fold lattice soliton solutions. To derive the high-order rational solutions, we further construct the high-order DT. Finally, we theoretically and graphically analyze these solutions, which exhibit lattice breather waves, W-shape lattice solitons, high-order lattice rogue waves (RW), and their interactions. [ABSTRACT FROM AUTHOR]

In this paper, we consider the non-linear Schrödinger equation in fibers with the presence of group velocity dispersion, selfphase modulation and second-order dispersion terms. Using the ansatz method, we derive its bright, dark, complexitons, Gaussian, and traveling wave solitons, respectively. Moreover, we provide the graphical analysis of some solutions in order to better understand their dynamical behavior. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the cubic Schrödinger equation with a bounded potential, which describes the propagation properties of optical soliton solutions. By employing an ansatz method, we precisely derive the bright and dark soliton solutions of the equation. Moreover, we obtain three classes of analytic periodic wave solutions expressed in terms of the Jacobi's elliptic functions including cn , sn and dn functions. Finally, by using a tan h function method, its complexitons solutions are derived in a very natural way. It is hoped that our results can enrich the nonlinear dynamical behaviors of the cubic Schrödinger equation with a bounded potential. [ABSTRACT FROM AUTHOR]

Under investigation in this work is a generalized nonlinear Schrödinger (NLS) equation with high-order dispersion and quintic nonlinear terms, which can describe a subpicosecond pulse propagation in optical fibers. By developing Hirota method, the bilinear form and analytical one- and two-soliton solutions are derived. Based on the analytical solutions, we give the corresponding soliton patterns to analyse dynamics of the pulse solitons. It shows that high order dispersion term may change the periodicity of propagation. The interaction of two pulse solitons is an elastic collision. By choosing suitable parameter values, we can obtain the two parallel solitons. It can be applied to improve transmission quality and capacity of information in optical fiber. [ABSTRACT FROM AUTHOR]

Under investigation in this paper is a coupled mixed derivative nonlinear Schrödinger equation, which can describe the pulse propagation in the femtosecond or picosecond regime of a birefringent optical fiber. Based on a Lax pair, we provide a Darboux transformation, and obtain the breather wave solutions. Then, a novel vector rogue wave solution is constructed by using Darboux-dressing transformation and asymptotic expansion. Those solutions exhibit some elastic and collision behaviors between a localized wave and a bright–dark soliton. Our works can be of importance in the theoretical experiments of the rogue wave generation mechanism and propagation trajectory. [ABSTRACT FROM AUTHOR]