Analysis of interaction between two solitons based on computerized symbolic computation

Abstract The study of soliton interaction is helpful to improve the quality and capacity of computer image processing. In this paper, using the computerized symbolic computation, the analytical two-soliton solutions are obtained by the Hirota bilinear method. Through choosing different parameters, the influences of them on soliton interactions are discussed. Interactions between solitons propagating in different directions are analyzed. Results are beneficial to the effective transmission of information in the optical coherence tomography system.

[1]  Anjan Biswas,et al.  Perturbation theory and optical soliton cooling with anti-cubic nonlinearity , 2017 .

[2]  Junkichi Satsuma,et al.  A Wronskian Representation of N-Soliton Solutions of Nonlinear Evolution Equations , 1979 .

[3]  N. C. Freeman.  Soliton Solutions of Non-linear Evolution Equations , 1984 .

[4]  Ali Saleh Alshomrani,et al.  Nonautonomous matter wave bright solitons in a quasi-1D Bose-Einstein condensate system with contact repulsion and dipole-dipole attraction , 2020, Appl. Math. Comput..

[5]  Anjan Biswas,et al.  Phase-shift controlling of three solitons in dispersion-decreasing fibers , 2019, Nonlinear Dynamics.

[6]  Anjan Biswas,et al.  Cubic–quartic optical solitons in Kerr and power law media , 2017 .

[7]  Anjan Biswas,et al.  Periodic attenuating oscillation between soliton interactions for higher-order variable coefficient nonlinear Schrödinger equation , 2019, Nonlinear Dynamics.

[8]  Anjan Biswas,et al.  Cubic–quartic optical solitons in Kerr and power law media , 2017 .

[9]  Anjan Biswas,et al.  Resonant optical solitons with quadratic-cubic nonlinearity by semi-inverse variational principle , 2017 .

[10]  Anjan Biswas,et al.  Optical soliton perturbation with anti-cubic nonlinearity by semi-inverse variational principle , 2017 .

[11]  Jerald J. Kovacic,et al.  An Algorithm for Solving Second Order Linear Homogeneous Differential Equations , 1986, J. Symb. Comput..

[12]  Anjan Biswas,et al.  Dromion-like soliton interactions for nonlinear Schrödinger equation with variable coefficients in inhomogeneous optical fibers , 2019, Nonlinear Dynamics.

[13]  Anjan Biswas,et al.  Optical solitons with nonlocal-parabolic combo nonlinearity by Lie symmetry analysis coupled with modified G′/G-expansion , 2019 .

[14]  Wenjun Liu,et al.  Some lump solutions for a generalized (3+1)-dimensional Kadomtsev-Petviashvili equation , 2020, Appl. Math. Comput..

[15]  Qin Zhou,et al.  Analytic study on triple-S, triple-triangle structure interactions for solitons in inhomogeneous multi-mode fiber , 2019, Appl. Math. Comput..

[16]  Qin Zhou,et al.  Lump and lump strip solutions to the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation , 2019, The European Physical Journal Plus.

[17]  Fritz Schwarz,et al.  Automatically determining symmetries of partial differential equations , 1985, Computing.

[18]  Anjan Biswas,et al.  Resonant 1-soliton solution in anti-cubic nonlinear medium with perturbations , 2017 .

[19]  Junping Wang,et al.  Simplified weak Galerkin and new finite difference schemes for the Stokes equation , 2018, J. Comput. Appl. Math..

[20]  Anjan Biswas,et al.  Darboux transformation and analytic solutions for a generalized super-NLS-mKdV equation , 2019, Nonlinear Dynamics.

[21]  Yuanyuan Yan,et al.  Stable transmission of solitons in the complex cubic-quintic Ginzburg-Landau equation with nonlinear gain and higher-order effects , 2019, Appl. Math. Lett..