Integrability and Multisoliton Solutions of the Reverse Space or/and Time Nonlocal Fokas-Lenells (FL) Equation

This paper studies reverse space or/and time nonlocal Fokas-Lenells (FL) equation, which describes the propagation of nonlinear light pulses in monomode optical fibers when certain higher-order nonlinear effects are considered, by Hirota bilinear method. Firstly, variable transformations from reverse space nonlocal FL equation to reverse time and reverse space-time nonlocal FL equations are constructed. Secondly, the one-, two- and three-soliton solutions of the reverse space nonlocal FL equation are derived through Hirota bilinear method, and the soliton solutions of reverse time and reverse space-time nonlocal FL equations are given through variable transformations. Dynamical behaviors of the multisoliton solutions are discussed in detail by analyzing their wave structures. Thirdly, asymptotic analysis of two- and three-soliton solutions of reverse space nonlocal FL equation is used to investigated the elastic interaction and inelastic interaction. At last, the Lax integrability and conservation laws of three types of nonlocal FL equations is studied. The results obtained in this paper possess new properties that different from the ones for FL equation, which are useful in exploring novel physical phenomena of nonlocal systems in nonlinear media.

Painlevé Analysis, Soliton Molecule, and Lump Solution of the Higher-Order Boussinesq Equation

The Painlevé integrability of the higher-order Boussinesq equation is proved by using the standard Weiss-Tabor-Carnevale (WTC) method. The multisoliton solutions of the higher-order Boussinesq equation are obtained by introducing dependent variable transformation. The soliton molecule and asymmetric soliton of the higher-order Boussinesq equation can be constructed by the velocity resonance mechanism. Lump solution can be derived by solving the bilinear form of the higher-order Boussinesq equation. By some detailed calculations, the lump wave of the higher-order Boussinesq equation is just the bright form. These types of the localized excitations are exhibited by selecting suitable parameters.

Soliton Solutions for a Nonisospectral Semi-Discrete Ablowitz–Kaup–Newell–Segur Equation

In this paper, we study a nonisospectral semi-discrete Ablowitz–Kaup–Newell–Segur equation. Multisoliton solutions for this equation are given by Hirota’s method. Dynamics of some soliton solutions are analyzed and illustrated by asymptotic analysis. Multisoliton solutions and dynamics to a nonisospectral semi-discrete modified Korteweg-de Vries equation are also discussed.

Complete integrability and complex solitons for generalized Volterra system with branched dispersion

In this paper, we show that complete integrability is preserved in a multicomponent differential-difference Volterra system with branched dispersion relation. Using the Hirota bilinear formalism, we construct multisoliton solutions for a system of coupled [Formula: see text] equations. We also show that one can obtain the same solutions through a periodic reduction starting from a two-dimensional completely integrable generalized Volterra system. For some particular cases, graphical representations of solitons are displayed and stability is discussed using an asymptotic analysis.

Painlevé integrability and multisoliton solutions of a generalized KdV system

The integrability of a generalized KdV model, which has abundant physical applications in many fields, is investigated by employing Painlevé test. Eventually, we discover a new generalized P-type KdV model in sense of WTCKruskal method. Subsequently, Hereman’s simplified bilinear method is used to examine the integrability of the resulted model. As a result, multiple soliton solutions of newly discovered model are formally obtained.