## 1 Introduction  
In the current century, many entropy problems have been expressed by using mathematical models that are nonlinear partial differential equations. New results in the last few years have shown that the relation between non-standard entropies and nonlinear partial differential equations can be applied on new nonlinear wave equations inspired by quantum mechanics. Nonlinear models of the celebrated Klein-Gordon and Dirac equations have been found to admit accurate time dependent soliton-like solutions with the shapes of the so-called q-plane waves. Such q-plane waves are generalizations of the complex exponential plane wave solutions of the linear Klein-Gordon and Dirac equations [1]. Wave progressing of soliton forming and its application in the differential equation has been noticeable in the last few years. The physical phenomena of nonlinear partial differential equations (NLPDEs) may connect to many areas of sciences, for example plasma physics, optical fibers, nonlinear optics, fluid mechanics, chemistry, biology, geochemistry, and engineering sciences. The nonlinear Schrodinger equations describe wave propagation in optical fibers with nonlinear impacts [2; 3; 4]. Various numeric and analytic techniques have been used to seek solutions for nonlinear differential equations such as the homotopy perturbation scheme [5], the Adams-Bashforth-Moulton method [6], the shooting technique with fourth-order Runge-Kutta scheme [7; 8; 9; 10], the group preserving method [11], the finite forward difference method [12; 13], the Adomian decomposition method [14; 15], the sine-Gordon expansion method [16; 17; 18], the modified auxiliary expansion method [19], the modified \(\exp(-\varphi\left(\xi\right))\) expansion function method [20; 21], the improved Bernoulli sub-equation method [22; 23], the Riccati-Bernoulli sub-ODE method [24], the modified exponential function method [25], the improved \(\tan(\phi\left(\xi\right)/2)\)[26; 27], the Darboux transformation method [28; 29], the double \(\left(\frac{G^{\prime}}{G^{\prime}},\frac{1}{G^{\prime}}\right)\) expansion method [30; 31], the \(\left(\frac{1}{G^{\prime}}\right)\) expansion method [32; 33], the decomposition Sumudu-like-integral transform method [34], and the inverse scattering method [35]. In recent years, many researchers have carried out investigations on the governing models in optical fibers. The nonlinear Schrodinger equation, involving cubic and quartic-order dispersion terms, has been investigated to seek the exact optical soliton solutions via the undetermined coefficients method [36], the modified Kudryashov approach [37], the complete discrimination system method [38], the generalized tanh function method [39], the sin-cosine method, as well as the Bernoulli equation approach [40], the semi-inverse variation method [41], a simple equation method [3], and the extended sinh-Gordon expansion method [42]. Now, optical solitons are the exciting research area of nonlinear optics studies, and this research field has led to tremendous advances in their extensive applications. It is identified that the dynamics of nonlinear optical solitons and Madelung fluids are based on the generalized nonlinear Schrodinger dispersive equation and resonant nonlinear Schrodinger dispersive equation. In the research of chirped solitons in Hall current impacts in the field of quantum mechanics, a specific resonant term must be given [43]. Dispersion and nonlinearity are the two key elements for the propagation of solitons over intercontinental ranges. Normally, group velocity dispersion (GVD) leveling with self-phase modulation in a sensitive way allows such solitons to maintain long distance travel. Now, it could occur that GVD is minuscule and therefore completely overlooked, so in this condition, the dispersion impact is rewarded for by third-order (3 OD) and fourth-order (4 OD) dispersion impacts. This is generally referred to as solitons that are cubic-quartic (CQ). This term was implemented in 2017 for the first time.