Anjan Biswas

Normal, AL 35762-4900, USA
Department of Physics, Chemistry and Mathematics, Alabama A&M University


Biswas A., Kara A. H., Ekici M., Zayed E., Alzahrani A. K., Belic M. R.
This paper implements a multiplier approach to exhibit conservation laws in magneto-optic waveguides that maintain anti-cubic as well as generalized anti-cubic forms of the nonlinear refractive index. Three conservation laws are retrieved for each form of nonlinearity. They are power, linear momentum and Hamiltonian. The conserved quantities are computed from their respective densities.
Keywords: solitons, conservation law, anti-cubic
Citation: Biswas A., Kara A. H., Ekici M., Zayed E., Alzahrani A. K., Belic M. R.,  Conservation Laws for Solitons in Magneto-optic Waveguides with Anti-cubic and Generalized Anti-cubic Nonlinearities, Regular and Chaotic Dynamics, 2021, vol. 26, no. 4, pp. 456-461
González-Gaxiola O., Biswas A., Asma M., Alzahrani A. K.
This paper numerically addresses optical dromions and domain walls that are monitored by Kundu – Mukherjee – Naskar equation. The Kundu – Mukherjee – Naskar equation is considered because this model describes the propagation of soliton dynamics in optical fiber communication system. The scheme employed in this work is Laplace – Adomian decomposition type. The accuracy of the scheme is $O(10^{-8})$ and the physical structure of the obtained solutions are shown by graphic illustration in order to give a better understanding on the dynamics of both optical dromions and domain walls.
Keywords: Kundu – Mukherjee – Naskar equation, optical dromions, domain walls, Laplace – Adomian decomposition method, Adomian polynomials
Citation: González-Gaxiola O., Biswas A., Asma M., Alzahrani A. K.,  Optical Dromions and Domain Walls with the Kundu – Mukherjee – Naskar Equation by the Laplace – Adomian Decomposition Scheme, Regular and Chaotic Dynamics, 2020, vol. 25, no. 4, pp. 338-348
Biswas A., Kara A. H., Zhou  Q., Alzahrani A. K., Belic M. R.
This paper reports conservation laws for highly dispersive optical solitons in birefringent fibers. Three forms of nonlinearities are studied which are Kerr, polynomial and nonlocal laws. Power, linear momentum and Hamiltonian are conserved for these types of nonlinear refractive index.
Keywords: conservation laws, highly dispersive solitons, birefringent fibers
Citation: Biswas A., Kara A. H., Zhou  Q., Alzahrani A. K., Belic M. R.,  Conservation Laws for Highly Dispersive Optical Solitons in Birefringent Fibers, Regular and Chaotic Dynamics, 2020, vol. 25, no. 2, pp. 166-177
Kudryashov N. A., Safonova D. V., Biswas A.
This paper considers the Radhakrishnan – Kundu – Laksmanan (RKL) equation to analyze dispersive nonlinear waves in polarization-preserving fibers. The Cauchy problem for this equation cannot be solved by the inverse scattering transform (IST) and we look for exact solutions of this equation using the traveling wave reduction. The Painlevé analysis for the traveling wave reduction of the RKL equation is discussed. A first integral of traveling wave reduction for the RKL equation is recovered. Using this first integral, we secure a general solution along with additional conditions on the parameters of the mathematical model. The final solution is expressed in terms of the Weierstrass elliptic function. Periodic and solitary wave solutions of the RKL equation in the form of the traveling wave reduction are presented and illustrated.
Keywords: Radhakrishnan – Kundu – Laksmanan equation, integrability, traveling waves, general solution, exact solution
Citation: Kudryashov N. A., Safonova D. V., Biswas A.,  Painlevé Analysis and a Solution to the Traveling Wave Reduction of the Radhakrishnan – Kundu – Lakshmanan Equation, Regular and Chaotic Dynamics, 2019, vol. 24, no. 6, pp. 607-614

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