Grey-Black Optical Solitons, Homoclinic Breather, Combined Solitons via Chupin Liu’s Theorem for Improved Perturbed NLSE with Dual-Power Law Nonlinearity

Abstract

In this article, we consider the improved perturbed nonlinear Schrödinger Equation (IP-NLSE) with dual power law nonlinearity, which arises in optical fibers and photovoltaic-photo-refractive materials. We found grey and black optical solitons of the governing equation by means of a suitable complex envelope ansatz solution. By using the Chupin Liu’s theorem (CLT) for the grey and black solitons, we evaluated new categories of combined optical soliton (COS) solutions to the IP-NLSE. The propagation behaviors for homoclinic breathers (HB), multiwaves and M-shape solitons will be analytically examined. All new analytical solutions will be found by an ansatz function scheme and suitable transformations. Multiwave solitons have been reported by using a three-waves technique. Furthermore, two kinds of interactions for M-shape soliton through exponential functions will be examined.

Analyzing Soliton Solutions of the Extended (3 + 1)-Dimensional Sakovich Equation

“…The presence of N is ascertainable within the framework of the balancing principle. Substituting (7) into Equation ( 6) and collecting similar terms, we derive the polynomial equation…”

“…Hence, the discovery of analytical solutions for these equations is crucial in comprehending their dynamics and elucidating the underlying mechanisms governing their existing states. Diverse researchers have successfully employed, developed, and refined a range of innovative approaches to obtain exact solutions for NPDEs, such as the modified and extended rational expansion method [1], the G ′ /(bG ′ + G + a)-expansion technique [2], similarity transformations [3], the Hirota bilinear method [4], the homogenouous balance method [5], the tanh technique [6], Chupin Liu's theorem [7], the first integral technique [8], auto-Backlund transformations [9], the sine-Gordon equation method [10], the modified G ′ /G -expansion method [11], the Riccati equation mapping method [12], the new Kudryashov technique [13], conservation laws [14,15], the Jacobian elliptic function expansion technique [16], Riccati-Bernoulli's sub-ODE technique [17], the sec h p function method [18], Painlevé integrability [19], and so on.…”