Airy–Bessel modulated self-similar rogue waves in a nonlinear Schrödinger equation model

Abstract

We construct explicit rogue wave solutions of the generalized nonlinear Schrödinger equation under Airy and Bessel-modulated nonlinearity and an external potential, by employing a multivariate self-similarity transformation. A set of conditions in the form of analytical relations among dispersion, external potential and nonlinearity have been found for rogue wave generation. Different dimensions of controllability of the rogue waves are also being explored by varying parameters associated with the nonlinearity coefficients by judiciously choosing the form of the parametric functions.

Keywords:

• rogue wave solutions
• generalized nonlinear Schrödinger equation
• Airy and Bessel-modulated nonlinearity
• self-similarity transformation

Additional information

Funding

KKD sincerely thanks UGC, Government of India, for financial support through FDP. TSR would like to thank DST, Government of India, for financial support through Fast Track Project (Young Scientist Award), during the course of this work.