Soliton Solutions of the Coupled Schrödinger-Boussinesq Equations for Kerr Law Nonlinearity

Abstract

In this paper, the coupled Schrödinger-Boussinesq equations (SBE) will be solved by the sech, tanh, csch, and the modified simplest equation method (MSEM). We obtain exact solutions of the nonlinear for bright, dark, and singular 1-soliton solution. Kerr law nonlinearity media are studied. Results have proven that modified simple equation method does not produce the soliton solution in general case. Solutions may find practical applications and will be important for the conservation laws for dispersive optical solitons.

The influence of the differential conformable operators through modern exact solutions of the double Schrödinger-Boussinesq system

“…which is in perfect coincidence with the once studies by Osman et al [38], Jawad and Abu-AlShaeer [39] and Eslami [29]. In plasma and laser physics, the important troubles framed by the interactivities between a complex nonlinear field of Schrödinger and a real field of Boussinesq have been exceedingly promoted [29,38,40,41].…”

“…When = 1 w , the resulted solutions (24)-( 51) reduce to a modern class of exact solutions of the double Schrödinger-Boussinesq system (2) with the traditional derivatives. Hence, be comparing our exact solutions (24)-( 51) with the results gained by Eslami [29], Jawad and Abu-AlShaeer [39], Bilige et al [55], and Kumar and Kaplan [56], we deduce that the solutions (24)-( 51) provide a novel general family of exact solutions for the double Schrödinger-Boussinesq system (2), which arises in varied problems related to plasma and laser physics. Moreover, the method utilized in this paper can be compared with other existing methods.…”