Optical solitons of new extended (3+1)-dimensional nonlinear Kudryashov's equation via ⁶-model expansion method

The newly developed (3+1)-dimensional nonlinear Kudryashov's equation offers a framework for studying the behavior of propagating modulated envelope signals and is particularly useful in the fields, where the propagation of wave-like phenomena is essential such as in the field of fluid dynamics, it helps to analyze phenomena like water waves and fluid flow behavior. In plasma physics, it helps to understand plasma instabilities and fusion device behavior. To obtain soliton solutions for the (3+1)-dimensional nonlinear Kudryashov's equation, the Phi(6)-model expansion method is employed to derive various forms of solitons, each with its own unique characteristics and properties. This analytical technique is known for its effectiveness in constructing soliton solutions for nonlinear equations and also provides constraints and conditions for the existence of these solitons. Furthermore, the study effectively emphasizes the physical significance of the proposed equation by presenting insightful graphical representations of the constructed soliton solutions. By considering a higher level of nonlinearity, this latest version of the equation presents a significant advancement in the understanding of soliton dynamics and provides a more comprehensive framework for studying wave phenomena. Our study delves into the fascinating realm of wave propagation and soliton dynamics, making a significant and original contribution to this field.