Hui-Min Yin

Bright optical solitons or light bullets for a (3 + 1)-dimensional generalized nonlinear Schrödinger equation with the distributed coefficients

Under investigation in this paper is a (3 + 1)-dimensional generalized nonlinear Schrodinger equation with the distributed coefficients for the spatiotemporal optical solitons or light bullets. Through the symbolic computation and Hirota method, one- and two-soliton solutions are derived. We also present the Backlund transformation, through which we derive the soliton solutions. When the gain/loss coefficient is the monotonically decreasing function for the propagation coordinate z, amplitude for the spatiotemporal optical soliton or light bullet decreases along z, while when the gain/loss coefficient is the monotonically increasing function for z, amplitude for the spatiotemporal optical soliton or light bullet increases along z. Directions of the solitons are different because the signs of imaginary parts of the frequencies are adverse. Based on the two-soliton solutions, elastic and inelastic collisions between the two spatiotemporal optical solitons or light bullets are derived under different conditions presented in the paper.

Solitons, bilinear Bäcklund transformations and conservation laws for a -dimensional Bogoyavlenskii-Kadontsev-Petviashili equation in a fluid, plasma or ferromagnetic thin film

Abstract In this paper, we investigate a -dimensional Bogoyavlenskii–Kadontsev–Petviashili equation in a fluid, plasma or ferromagnetic thin film. Through the Bell polynomials, Hirota method and symbolic computation, the one- and two-kink-soliton solutions are derived. Bäcklund transformation, Lax pair and conservation laws are presented. Elastic collisions including the oblique, parallel, unidirectional and bidirectional collisions between the two-kink solitons are discussed. In addition, the relation between the velocities and wave numbers of the two-kink solitons are analysed. When wave numbers , the velocities in the x axis, increase with wave numbers increasing. With increasing, increase when , while decrease when . , the velocities in the y axis, increase with increasing and decreasing.

Solitons and bilinear Bäcklund transformations for a (3+1)-dimensional Yu–Toda–Sasa–Fukuyama equation in a liquid or lattice

Abstract In this paper, we investigate a ( 3 + 1 ) -dimensional Yu–Toda–Sasa–Fukuyama equation for the interfacial wave in a two-layer liquid or elastic quasiplane wave in a lattice. Through the Bell polynomials, symbolic computation and Hirota method, the one and two bell-soliton solutions are derived. Backlund transformation is presented. Parallel collision between the two solitons exists when the soliton directions are the same. Oblique collision appears between the two solitons with different soliton directions.

Rogue waves and lump solitons for a -dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics

Abstract Under investigation is a -dimensional B-type Kadomtsev–Petviashvili equation, which has applications in the propagation of non-linear waves in fluid dynamics. Through the Hirota method and the extended homoclinic test technique, we obtain the breather-type kink soliton solutions and breather rational soliton solutions. Rogue wave solutions are derived, which come from the derivation of breather rational solitons with respect to x. Amplitudes of the breather-type kink solitons and rogue waves decrease with a non-zero parameter in the equation, , increasing when . In addition, dark rogue waves are derived when . Furthermore, with the aid of the Hirota method and symbolic computation, two types of the lump solitons are obtained with the different choices of the parameters. We graphically study the lump solitons related to the parameter , and amplitude of the lump soliton is negatively correlated with when .

Lump waves and breather waves for a (3+1)-dimensional generalized Kadomtsev–Petviashvili Benjamin–Bona–Mahony equation for an offshore structure

In this paper, we investigate a (3+1)-dimensional generalized Kadomtsev–Petviashvili Benjamin–Bona–Mahony equation, which describes the fluid flow in the case of an offshore structure. By virtue of...

Numerical solutions of a variable-coefficient nonlinear Schrödinger equation for an inhomogeneous optical fiber

Abstract This paper investigates a variable-coefficient nonlinear Schrodinger equation for an inhomogeneous optical fiber. Numerical one- and two-solitonic envelopes of the electrical field via the fourth-order split-step Runge–Kutta, split-step Fourier and Runge–Kutta methods with equal grids in the τ axis and equal grids in the ξ axis are graphically presented, respectively, where τ and ξ represent the retarded time and normalized distance along the fiber. 2-norm of the relative errors between the analytical solutions under the Painleve integrability condition and numerical solutions are given, where the CPU time is also shown. Relative errors and CPU time of the numerical one- and two-soliton solutions with equal grids in the ξ axis are bigger than those with equal grids in the τ axis, which does not mean that the results with equal grids in the ξ axis are infeasible. Compared with the numerical solutions with equal grids in the τ axis, those with equal grids in the ξ axis are closer to the analytical solutions without the Painleve integrability condition. With respect to the relative errors and CPU time, one could choose the split-step Fourier method to derive the numerical one-soliton solutions, while the numerical two-soliton solutions are gotten with the RK method. The attenuation coefficient makes the amplitudes of the solitons decrease, the group velocity dispersion coefficient leads to the periodic solitons, while the effect of the attenuation coefficient is more obvious than that of the nonlinearity parameter. Effects of η R , 1 and η I , 1 on the solitonic weak interaction between the two solitons are investigated: Solitonic weak interaction between the two solitons enhances with η R , 1 and η I , 1 increasing, where η R , 1 and η I , 1 are the frequencies of the two solitons.

Bäcklund transformation, analytic soliton solutions and numerical simulation for a (2+1)-dimensional complex Ginzburg–Landau equation in a nonlinear fiber

In this paper, we investigate a nonlinear fiber described by a (2+1)-dimensional complex Ginzburg–Landau equation with the chromatic dispersion, optical filtering, nonlinear and linear gain. Backlund transformation in the bilinear form is constructed. With the modified bilinear method, analytic soliton solutions are obtained. For the soliton, the amplitude can decrease or increase when the absolute value of the nonlinear or linear gain is enlarged, and the width can be compressed or amplified when the absolute value of the chromatic dispersion or optical filtering is enhanced. We study the stability of the numerical solutions numerically by applying the increasing amplitude, embedding the white noise and adding the Gaussian pulse to the initial values based on the analytic solutions, which shows that the numerical solutions are stable, not influenced by the finite initial perturbations.

Pfaffian solutions for the (3+1)-dimensional nonlinear evolution equation in a fluid/plasma/crystal and the (2+1)-dimensional Sawada–Kotera equation in a liquid

For the (3+1)-dimensional nonlinear evolution equation in a plasma, crystal or fluid, the Pfaffian solutions are obtained via the Bell polynomials, symbolic computation and Hirota method. Amplitudes and velocities of the solitons are discussed, respectively, as well as the conditions on whether the collisions are overtaking or head-on in the fluid/plasma/crystal. If the product of four wave numbers is greater than 0, collisions are overtaking, or else, head-on. For the (2+1)-dimensional Sawada–Kotera equation in a liquid, we discuss that amplitudes and velocities of the solitons, as well as the conditions of solitonic collisions. Hereby, there only exist the overtaking collisions between the solitons in such a liquid because the sign of l1 + l2 is the same as l13 + l 23, where l1 and l2 are the wave numbers in the liquid. Figures showing the overtaking and head-on collisions for the two and three solitons in the fluid/plasma/crystal are also presented.

Stochastic soliton solutions for the (2+1)-dimensional stochastic Broer–Kaup equations in a fluid or plasma

Abstract In this paper, we investigate the ( 2 + 1 ) -dimensional stochastic Broer–Kaup equations for the shallow water wave in a fluid or electrostatic wave in a plasma. Through the symbolic computation, Hirota method and white noise functional approach, the stochastic one- and two-soliton solutions are derived. Through the stochastic one soliton solutions, we derive the velocities of solitons, respectively, and graphically investigate the effect of the white noise on the velocities. The effects of the Gaussian white noise on the dynamic properties of the solitons are discussed. We get that the white noise poses some influence to the soliton of U , where U is related to the horizontal velocity of the water wave, with which the soliton of U would vanish with time instead of propagating stably. On the contrary, transmission of the soliton of V presents certain stability no matter whether the white noise exists, where V is related to the horizontal elevation of the water wave. Figures are displayed for the elastic collisions between the two oscillating-, parabolic- and bell-type solitons, respectively. In addition, collisions are shown to be elastic through the asymptotic analysis.