Yi-Tian Gao

Solitons and Backlund transformation for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation in fluid dynamics

Abstract Under investigation in this paper is a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation, which describes the propagation of nonlinear waves in fluid dynamics. Bilinear form and Backlund transformation are derived by virtue of the Bell polynomials. Besides, the one- and two-soliton solutions are constructed via the Hirota method.

Rogue waves for the generalized nonlinear Schrödinger–Maxwell–Bloch system in optical-fiber communication

Abstract In this letter, a generalized nonlinear Schrodinger–Maxwell–Bloch system is investigated, which can be used to describe the solitons in optical fibers. By virtue of the generalized Darboux transformation, higher-order rogue-wave solutions are derived. Rogue-wave propagation and interaction are analyzed: (1) Complex envelope of the field, q , appears as a bright rogue wave, the measure of the polarization of the resonant medium, p , is a bright-dark rogue wave while the extant of the population inversion, η , is a dark rogue wave; (2) Group velocity inhomogeneity and the linear and Kerr nonlinearity inhomogeneity affect q , p and η more than the other parameters do; (3) Character of the interaction between the propagating field and erbium atoms, the gain or loss term and the linear and Kerr nonlinearity inhomogeneous parameter affect the interaction range of the second-order rogue waves.

Breather-to-soliton transition for a sixth-order nonlinear Schrödinger equation in an optical fiber

Abstract In this letter, breather-to-soliton transition is studied for an integrable sixth-order nonlinear Schrodinger equation in an optical fiber. Constraint for the breather-to-soliton transition is given. Breathers could be transformed into the different types of solitons, which are determined by the values of the real and imaginary parts of the eigenvalues in the Darboux transformation. Interactions of the breathers and breathers, of the breathers and solitons, as well as of the solitons and solitons, are graphically presented.

Solitons for a (2+1)-dimensional Sawada–Kotera equation via the Wronskian technique

Abstract Under investigation in this letter is a (2+1)-dimensional Sawada–Kotera equation. Solitons are obtained by virtue of the Wronskian technique. Via the fourth- and sixth-order Plucker relations for the Wronskian, we give a proof for the N -soliton solutions. Interactions between/among the two/three solitons are investigated, and it seems that those interactions are elastic.

Nonautonomous solitons and Wronskian solutions for the (3+1)-dimensional variable-coefficient forced Kadomtsev-Petviashvili equation in the fluid or plasma

Abstract Under investigation in this paper is a ( 3 + 1 )-dimensional variable-coefficient forced Kadomtsev–Petviashvili equation which can describe the nonautonomous solitons in such areas as fluids and plasmas. The first- and second-order nonautonomous solitons are constructed via the Hirota bilinear method. Propagation and interaction of the nonautonomous solitons are analyzed. Perturbation coefficient affects the amplitude of the nonautonomous soliton. The background where the nonautonomous soliton exists can be influenced by the external force coefficient. Breathers and resonant interaction, which are the special interaction structures for the second-order nonautonomous solitons, are also presented. Nonuniformity coefficient influences the period of the breather. For the resonant interaction, the two nonautonomous solitons merge into a single solitary wave and form three branches, the amplitudes of which are influenced by the perturbation coefficient. Solutions in terms of the Wronskian determinants are constructed and verified via the direct substitution into the bilinear form.