Symmetry Solutions and Conservation Laws for the 3D Generalized Potential Yu-Toda-Sasa-Fukuyama Equation of Mathematical Physics

Inhomogeneous liquid may be argued to inhomogeneous density or induced by an external field. It is a type of the commonly seen fluids. Heterogeneous medium, which stands to, by heterogeneous medium (HM). As a realistic example, the Earth’s atmosphere, as a whole, it is blue a heterogeneous mixture. Further, the liquid formed from oil and water, which is with non-uniform composition, is immiscible HM. The study of the dynamics of clouds, as HM fluid, is of great interest in depicting many natural phenomena. It is recognized that petroleum pollutants were being discharged in marine waters worldwide, from oil spills. So, methods for assessing petroleum load and a discussion about the concerns of these loads were presented. Due to the wide spread of the applications of the heterogeneous fluid (or liquid) in nature, this motivated us to study, here, a prototype example. The model equation that describes the interaction of two-layer liquid was constructed by (3+1)-dimensional Yu-Toda-Sasa-Fukuyama (3D-YTSFE), which is an integro-differential equation. A generalized 3D-YTSFE with constant or time-dependent coefficients was intensively studied the literature. Here, we are concerned with the study of the dynamics of two-layer heteroogeneous liquid with space and time-dependent coefficients. That is, model equation constructed here is inhomogeneous-non-autonomous generalized 3D-YTSFE. The problem considered, in the present work, is completely novel and was not studied previously. This may be argued to the fact that it cannot be amenable by the known methods in the literature. On the other hand, the derivations are not straightforward. We solve the equations obtained, which contain arbitrary functions and their space and time derivatives. So, compatibility equations are needed, that will be illustrated, here, in detail. Exact solutions of the proposed model equation are found via the extended unified method. A variety of similarity solutions are found in polynomial and rational forms in an auxiliary function. They are evaluated numerically and are represented in graphs. It is shown that they reveal abundant novel waves geometric structures. They are classified as cylindrical soliton, molar soliton, soliton with support and double branches, dromian structure, lattice wave with tunneling, capillary wave, and chaotic solutions.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Symmetry Solutions and Conservation Laws for the 3D Generalized Potential Yu-Toda-Sasa-Fukuyama Equation of Mathematical Physics

Cited by 2 publications

References 43 publications

On the dynamics of exact solutions to a (3+1)-dimensional YTSF equation emerging in shallow sea waves: Lie symmetry analysis and generalized Kudryashov method

On the dynamics of exact solutions to a (3+1)-dimensional YTSF equation emerging in shallow sea waves: Lie symmetry analysis and generalized Kudryashov method

Complex physical phenomena of a generalized (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation in a two-layer heterogeneous liquid

Contact Info

Product

Resources

About