Solitons, breathers, and rogue waves on photorefractive backgrounds: exact solutions and NLSE-NLSE transformations

Abstract

This paper presents an analytical technique and NLSE-NLSE transformations to discover new spatial soliton solutions, Akhmediev breather (AB) solutions, and first-order rogue waves in photorefractive media backgrounds. The study includes non-centrosymmetric and centrosymmetric photorefractive media, as well as media exhibiting both linear and quadratic electro-optic effects. Using the proposed technique, we discovered exact spatial soliton solutions that can be steered in all these media. Exact AB solutions for all three media types were derived using NLSE-NLSE transformations. We found that AB solutions exhibit a plane-wave profile when photorefractive nonlinearity is high and transform into Peregrine solitons (first-order rogue waves) when nonlinearity is low. By taking the limit of the electro-optic parameter to zero from the AB solutions, we derived analytical solutions for first-order rogue waves across all the media. The characteristics of spatial solitons, AB, and first-order rogue waves, as examined in each media background, show significant differences according to the intrinsic nature of each medium. The NLSE-NLSE transformation has proven to be a powerful and invertible tool, and, in addition to its application in the AB case, can also be widely used to recover spatial soliton and first-order rogue wave solutions found in this study.