Anjan Biswas
Publications:
Kudryashov N. A., Safonova D. V., Biswas A.
Painlevé Analysis and a Solution to the Traveling Wave Reduction of the Radhakrishnan – Kundu – Lakshmanan Equation
2019, vol. 24, no. 6, pp. 607614
Abstract
This paper considers the Radhakrishnan – Kundu – Laksmanan (RKL) equation to
analyze dispersive nonlinear waves in polarizationpreserving 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.
