Soliton dynamics in the three-spine $$\alpha $$α-helical protein with inhomogeneous effect

We study a three-coupled variable-coefficient nonlinear Schrödinger equation, which describes soliton dynamics in the three-spine $$\alpha $$α-helical protein with inhomogeneous effect, and analytically obtain multi-soliton solutions, whose formation originates from the dynamical balance between the dispersion owing to the resonant interaction of intrapeptide dipole vibrations and the nonlinear interaction provided by those vibrations with the local displacements of the peptide groups. Using these analytical solutions as initial solutions, we discuss the dynamical behaviors of solitonic interactions and the influence of the protein inhomogeneity on shape-changing collisions of solitons by direct numerical simulations.

[1]  Yi-Xiang Chen,et al.  Nonlinear tunnelling effect of combined Kuznetsov–Ma soliton in (3+1)-dimensional $${{\varvec{\mathcal {PT}}}}$$PT-symmetric inhomogeneous nonlinear couplers with gain and loss , 2015 .

[2]  Akira Hasegawa,et al.  Nonautonomous solitons in external potentials. , 2007, Physical review letters.

[3]  Y. Feng,et al.  Quantum mechanics in nonlinear systems , 2005 .

[4]  A. Hasegawa,et al.  Soliton management in the nonlinear Schrödinger equation model with varying dispersion, nonlinearity, and gain , 2000 .

[5]  X. Pang,et al.  Influences of structure disorder and temperature on properties of proton conductivity in hydrogen-bond molecular systems , 2007 .

[6]  Anjan Biswas,et al.  Bright and dark solitons in optical metamaterials , 2014 .

[7]  Anjan Biswas,et al.  Thirring combo-solitons with cubic nonlinearity and spatio-temporal dispersion , 2016 .

[8]  Hasegawa,et al.  Novel soliton solutions of the nonlinear Schrodinger equation model , 2000, Physical review letters.

[9]  Y. Kivshar,et al.  Dynamics of coupled dark and bright optical solitons. , 1989, Optics letters.

[10]  A. Davydov,et al.  The role of solitons in the energy and electron transfer in one-dimensional molecular systems , 1981 .

[11]  Bo Tian,et al.  Solitonic excitations and interactions in an α-helical protein modeled by three coupled nonlinear Schrödinger equations with variable coefficients , 2010 .

[12]  L. Brizhik,et al.  Electromagnetic Radiation Influence on Nonlinear Charge and Energy Transport in Biosystems , 1999, Journal of biological physics.

[13]  X. Pang,et al.  Improvement of the Davydov theory of bioenergy transport in protein molecular systems. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  Shan Liu,et al.  Dark optical solitons in quadratic nonlinear media with spatio-temporal dispersion , 2015 .

[15]  Zachariah Sinkala,et al.  Soliton/exciton transport in proteins. , 2006, Journal of theoretical biology.

[16]  Qin Zhou,et al.  Exact optical solitons in metamaterials with cubic–quintic nonlinearity and third-order dispersion , 2015 .

[17]  L Brizhik,et al.  Solitons in alpha-helical proteins. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Bo Qin,et al.  Solitonic Excitations and Interactions in the Three-Spine Alpha-Helical Protein with Inhomogeneity , 2011, SIAM J. Appl. Math..

[19]  Qiuping Zhu,et al.  Bright, dark and singular optical solitons in a cascaded system , 2015 .

[20]  Xiao-feng.  Comment on "Thermodynamic properties of alpha -helix protein: A soliton approach" , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  Hui-Qin Hao,et al.  Coherently coupled solitons, breathers and rogue waves for polarized optical waves in an isotropic medium , 2015 .

[22]  Hai-Ping Zhu,et al.  Controllable behaviors of spatiotemporal breathers in a generalized variable-coefficient nonlinear Schrödinger model from arterial mechanics and optical fibers , 2015 .

[23]  Y. Kivshar,et al.  Symbiotic optical solitons and modulational instability , 1991 .

[24]  Shin,et al.  Correlation between the kolmogorov-sinai entropy and the self-diffusion coefficient in simple liquids , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.