Qi-Xing Qu

Solitonic excitations and interactions in an α-helical protein modeled by three coupled nonlinear Schrödinger equations with variable coefficients

Governing the molecular excitations associated with bioenergy transport in an α-helical protein through the soliton modes, three-coupled higher-order nonlinear Schrodinger equations with variable coefficients are investigated via symbolic computation. Using Bell polynomials, a bilinear form and Backlund transformation are derived for this model. Furthermore, explicit N-soliton solutions are constructed in terms of the double Wronskian determinant. Solitonic excitations are found to remain stable against the disorders of the parameters under certain constraints. Finally, propagation characteristics and interactions of the solitonic excitations are discussed. Soliton amplitudes are related to the energy modulation coefficients, and both the soliton properties and energy distribution during the interactions are affected by the inhomogeneity coefficients of the protein with time-dependent disorders.

A new approach to the analytic soliton solutions for the variable-coefficient higher-order nonlinear Schrödinger model in inhomogeneous optical fibers

In this paper, for the propagation of the ultra-short optical pulses in the normal dispersion regime of inhomogeneous optical fibers, the variable-coefficient higher-order nonlinear Schrödinger equation is investigated. A bilinear form and analytic soliton solutions are obtained with the help of the modified Hirota method and symbolic computation. Through choosing the different dispersion profiles of the inhomogeneous optical fibers, relevant properties of the soliton solution are graphically discussed. Parabolic-type evolution of the soliton is observed. Additionally, periodic and s-shaped solitons are derived, respectively. Finally, a possibly applicable compression technique for the dark soliton is proposed. The results might be of potential application to soliton control, soliton compression, signal amplification and dispersion management.

Solitonic Excitations and Interactions in the Three-Spine

With consideration of the molecular structure containing three hydrogen spines and the existence of the protein inhomogeneity, the bioenergy transport mechanism in the

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-Helical Protein with Inhomogeneity

-helical protein is investigated, which is described by the three-coupled perturbed nonlinear Schrodinger equations. Via symbolic computation, an infinite number of conservation laws and multisoliton solutions are derived for the underlying soliton dynamics with certain constraints. Through the asymptotic analysis, the solitonic excitations are shown to be influenced by the thermal and structural inhomogeneities, which can convert the rectilinear propagations into the curvilinear propagations and make the energy fluctuate. In particular, the shape changing collision and periodic interference of the solitonic excitations are analyzed. Energy exchange among the three hydrogen bonding spines is demonstrated, revealing the potential connection among three spines that used to be ignored in the one-spine model. The solitonic interference ...

Bäcklund transformation, Lax pair, and solutions for the Caudrey–Dodd–Gibbon equation

By using Bell polynomials and symbolic computation, we investigate the Caudrey–Dodd–Gibbon equation analytically. Through a generalization of Bells polynomials, its bilinear form is derived, based on which, the periodic wave solution and soliton solutions are presented. And the soliton solutions with graphic analysis are also given. Furthermore, Backlund transformation and Lax pair are derived via the Bells exponential polynomials. Finally, the Ablowitz-Kaup-Newell-Segur system is constructed.

Soliton solutions and Bäcklund transformation for the complex Ginzburg–Landau equation

Abstract Symbolically investigated in this paper is the complex Ginzburg–Landau (CGL) equation. With the Hirota method, both bright and dark soliton solutions for the CGL equation are obtained simultaneously. New Backlund transformation in the bilinear form is derived. Relevant properties and features are discussed. Solitons can be compressed (amplified) when the nonlinear (linear) dispersion effect is enhanced. Meanwhile, central frequency of the soliton can be affected by the nonlinear and linear dispersion effects. Besides, directions of the movement for the soliton central frequency can be adjusted. Results of this paper would be of certain value to the studies on the soliton compression and amplification.

Soliton solutions and Bäcklund transformation for the generalized inhomogeneous coupled nonlinear Schrödinger equations via symbolic computation

The generalized inhomogeneous coupled nonlinear Schrodinger (CNLS) equations are under investigation in this paper. Based on the Hirota method, the bilinear form and analytic one-, two- and N-soliton solutions are obtained, of which some properties are discussed simultaneously. Furthermore, with symbolic computation, the Backlund transformation and some sample soliton solutions for the inhomogeneous CNLS equations are given.

Symbolic-Computation Study on the (2+1)-Dimensional Dispersive Long Wave System

Under investigation in this paper is the (2+1)-dimensional dispersive long wave system, which describes the hydrodynamics of wide channels or open seas of finite depth. Its bilinear form is derived with the generalized Bell polynomials. New analytic solutions are obtained via symbolic computation, based on which the propagation of the water waves is analyzed graphically and the different phenomena of fission and fusion are revealed. Additionally, the bilinear auto-Backlund transformation is obtained by the generalized Bell polynomials.

Soliton solutions for a variable-coefficient Korteweg?de Vries equation in fluids and plasmas

In this paper, we investigate a variable-coefficient Korteweg?de Vries (vc-KdV) equation, which can be used to describe the propagation of nonlinear waves in fluids, plasmas and other fields. Through the rational transformation and Hirota method, new soliton solutions to the vc-KdV equation are derived. On the basis of those soliton solutions, three types of collisions are obtained: overtaking collision between two unidirectional solitons, head-on collision between two bidirectional ones and collision between moving and stationary solitons. These collisions are proved to be elastic through asymptotic analysis, and figures are plotted which show that they are indeed elastic except for a phase shift.