This paper secures solitary waves, shock waves and singular solitary waves for the Boussinesq equation, which is studied with the inclusion of surface tension. The method of undetermined coefficients has yielded such waves. The Lie symmetry analysis has introduced a fresh perspective to the model. Conserved densities and corresponding conserved quantities are computed using the multiplier approach.
In the present investigation, we employed the Jacobi elliptic function (JEF) method to invoke the perturbed nonlinear Schrödinger equation with self-steepening (SS), self-phase modulation (SPM), and group velocity dispersion (GVD), which govern the propagation of solitonic pulses in optical fibres. The proposed algorithm proves the existence of the family of solitons in optical fibers. Consequently, chirped and chirp free W-shaped bright, dark soliton solutions are obtained from dn(ξ ), cn(ξ ) and sn(ξ ) functions. The final results are displayed in three-dimensional plots with specific physical values of GVD, SPM and SS for an optical fiber.
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