Abstract
The Z1-Z4 transformations proposed in our previous papers have acquired remarkable success in the field of linear partial differential equations, general solutions of a large number of typical equations were obtained for the first time, and exact solutions of many definite solution problems of general significance were also successfully obtained. In this paper we will present the Z5 transformation and use it to get the general solutions of a variety of first-order quasi-linear partial differential equations and, for the first time, to obtain analytical solutions of a class of second-order quasi-linear partial differential equations containing arbitrary functions. Using the general solutions, we obtain exact solutions of two definite solution problems. By comparison we find that the general solutions of some first-order quasi-linear partial differential equations that can be obtained using the characteristic equation method are incomplete.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Partial Differential Equations in Applied Mathematics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
