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2-D solitary waves in thermal media with nonsymmetric boundary conditions

Journal Article


Abstract


  • Optical solitary waves and their stability in focusing thermal optical media, such as lead glasses, are studied numerically and theoretically in (2 + 1) dimensions. The optical medium is a square cell and mixed boundary conditions of Newton cooling and fixed temperature on different sides of the cell are used. Nonlinear thermal optical media have a refractive index which depends on temperature, so that heating from the optical beam and heat flow across the boundaries can change the refractive index of the medium. Solitary wave solutions are found numerically using the Newton conjugate-gradient method, while their stability is studied using a linearized stability analysis and also via numerical simulations. It is found that the position of the solitary wave is dependent on the boundary conditions, with the center of the beam moving toward the warmer boundaries, as the parameters are varied. The stability of the solitary waves depends on the symmetry of the boundary conditions and the amplitude of the solitary waves.

Publication Date


  • 2019

Citation


  • Louis, S. A., Marchant, T. R. & Smyth, N. F. (2019). 2-D solitary waves in thermal media with nonsymmetric boundary conditions. Studies in Applied Mathematics, 142 (4), 586-607.

Scopus Eid


  • 2-s2.0-85056155764

Number Of Pages


  • 21

Start Page


  • 586

End Page


  • 607

Volume


  • 142

Issue


  • 4

Place Of Publication


  • United States

Abstract


  • Optical solitary waves and their stability in focusing thermal optical media, such as lead glasses, are studied numerically and theoretically in (2 + 1) dimensions. The optical medium is a square cell and mixed boundary conditions of Newton cooling and fixed temperature on different sides of the cell are used. Nonlinear thermal optical media have a refractive index which depends on temperature, so that heating from the optical beam and heat flow across the boundaries can change the refractive index of the medium. Solitary wave solutions are found numerically using the Newton conjugate-gradient method, while their stability is studied using a linearized stability analysis and also via numerical simulations. It is found that the position of the solitary wave is dependent on the boundary conditions, with the center of the beam moving toward the warmer boundaries, as the parameters are varied. The stability of the solitary waves depends on the symmetry of the boundary conditions and the amplitude of the solitary waves.

Publication Date


  • 2019

Citation


  • Louis, S. A., Marchant, T. R. & Smyth, N. F. (2019). 2-D solitary waves in thermal media with nonsymmetric boundary conditions. Studies in Applied Mathematics, 142 (4), 586-607.

Scopus Eid


  • 2-s2.0-85056155764

Number Of Pages


  • 21

Start Page


  • 586

End Page


  • 607

Volume


  • 142

Issue


  • 4

Place Of Publication


  • United States