Li-Cai Liu

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.

Bell-polynomial approach and N-soliton solution for the extended Lotka-Volterra equation in plasmas

Symbolically investigated in this paper is the extended Lotka–Volterra (ELV) equation, which can govern the kinetics of the discrete peaks of the weak Langmuir turbulence in plasmas without the linear damping and random noise. Binary Bell polynomials are applied to the bilinearization of the discrete system. Bilinear Backlund transformation of the ELV equation is constructed. N-soliton solution in terms of the extended Casorati determinant is also presented and verified. Propagation and interaction behaviors of the Langmuir turbulence are analyzed. It is demonstrated that the number of the interacting Langmuir waves can influence the soliton velocity and amplitude as well as the collision phase shift. Graphic illustrations of the solitonic collisions show that the repulsion effects and nonlinear interactions are also associated with the number of the interacting Langmuir waves.

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 ...

Multi-Soliton Solutions for an Inhomogeneous Nonlinear Schrödinger– Maxwell–Bloch System in the Erbium-Doped Fiber

Under investigation in this paper is an inhomogeneous nonlinear Schrödinger-Maxwell-Bloch system with variable dispersion and nonlinear effects, which describes the propagation of optical pulses in an inhomogeneous erbium-doped fiber. Under certain coefficient constraints, multi-soliton solutions are obtained by the Hirota method and symbolic computation. Evolution and interaction of the solitons are plotted, and the self-induced transparency effect caused by the doped erbium atoms is found to lead to the change of the soliton velocity and phase. Overall phase shift can be observed when the parameter accounting for the interaction between the silica and doped erbium atoms is taken as a constant.

Reductions and Solutions of Two Types of Coupled Nonlinear Evolution Equations in Optical Fibers and Fluid Dynamics

Abstract Under investigation in this paper are the coupled nonlinear Schrödinger equations (CNLSEs) and coupled Burgers-type equations (CBEs), which are, respectively, a model for certain birefringent optical fibers Raman-scattering, Kerr and gain/loss effects, and a generalized model in fluid dynamics. Special attention should be paid to the existing claim that the solitons for the CNLSEs do not exist. Through certain dependent-variable transformations, the CNLSEs are reduced to a Manakov system and the CBEs are linearized. In that way, some new solutions of the CNLSEs and CBEs are obtained via symbolic computation. Especially the one-dark-soliton-like solutions for the CNLSEs have been found, against the existing claim. Abstract Under investigation in this paper are the coupled nonlinear Schr¨odinger equations (CNLSEs) and coupled Burgers-type equations (CBEs), which are, respectively, a model for certain birefringent optical fibers Raman-scattering, Kerr and gain/loss effects, and a generalized model in fluid dynamics. Special attention should be paid to the existing claim that the solitons for the CNLSEs do not exist. Through certain dependent-variable transformations, the CNLSEs are reduced to a Manakov system and the CBEs are linearized. In that way, some new solutions of the CNLSEs and CBEs are obtained via symbolic computation. Especially the one-dark-soliton-like solutions for the CNLSEs have been found, against the existing claim.