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This study is focusing on the integrable (3+1)-dimensional equation that combines the potential Kadomtsev-Petviashvili (pKP) equation with B-type Kadomtsev-Petviashvili (BKP) equation, also known as the pKP-BKP equation. The idea of combining integrable equations has the potential to produce a variety of unexpected outcomes such as resonance of solitons. This article provides a wide range of alternative exact solutions for the pKP-BKP equation in three dimensional form, including dark solitons, singular solitons, singular periodic solutions, Jacobi elliptic function (JEF) solutions, rational solutions and exponential solution. The improved modified extended (IME) tanh function method is employed to investigate these solutions. All of the obtained solutions for the investigated model are presented using the Wolfram Mathematica program. To further help in understanding the solutions' physical characteristics and dynamic structure, the article provides visual representations of some derived solutions using 2D representation in addition to the 3D graphs via symbolic computation. This article aims to use a potent strategy using a powerful scheme to derive different solutions with various structures. Additionally, the results greatly improve and enhance the literature's solutions to a combined pKP-BKP equation and allow deep understanding of the nonlinear dynamic system through different exact solutions.

We have introduced various novel soliton waves and other analytic wave solutions for nonlinear Schrödinger equation with cubic, quintic, septic, and nonic nonlinearities. The modified extended direct algebraic method governs the transmission of various solitons with different effects. The combination of this system enables the obtaining of analytical soliton solutions with some unique behaviors, including bright, dark, and mixed dark-bright soliton solutions; singular soliton solutions; singular periodic, exponential, rational wave solutions; and Jacobi elliptic function solutions. These results realize the stability of the nonlinear waves' propagation in a high-nonlinear-dispersion medium that is illustrated using 2D and 3D visuals and contour graphical diagrams of the output solutions. This research focused on determining exact soliton solutions under certain parameter conditions and evaluating the stability and reliability of the soliton solutions based on the used modified extended direct algebraic method. This will be useful for many various domains in technology and physics, such as biology, optics, and plasma physical science. At the end, we use modulation instability analysis to assess the stability of the wave solutions obtained.

Because it is used in communication and information technology, the propagation of pulses in optical fibers has become a significant research subject in recent years. Mathematical models have been created to describe the behaviors of optical solitons in optical fibres, such as the Kaup-Newell equation, the nonlinear Schrödinger equation with various types of nonlinearity, and others. A model among these is the newly generalized nonlinear Schrödinger equation with triple refractive index and non-local nonlinearity. To secure optical solitons for a particular case of this novel model, we used the improved modified extended tanh function approach. Different solutions have been acquired such as bright solitons, dark solitons, singular solitons, singular periodic solutions, trigonometric solutions, and hyperbolic solutions. Some of the discovered solutions are shown in 2D and 3D graphs for better comprehension and demonstration.

Optical soliton solutions in birefringent fibers and other analytic solutions for Sasa-Satsuma equation with Kerr law nonlinearity are investigated using extended F-expansion method. Bright, dark, singular, combo bright-singular, combo dark-singular and combo singular soliton solutions are extracted. Also, periodic, rational and Jacobi elliptic functions solutions are derived. Finally, we offer some 3D, 2D and contour plots to illustrate the nature of the provided solutions.