Finding Some General Exact Solutions to the Non-Linear Monge-Ampere Equations (PDEs)

Steve Anglin; Sc.M

doi:https://doi.org/10.14445/22315373/IJMTT-V65I10P513

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 10 | Year 2019 | Article Id. IJMTT-V65I10P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I10P513

Finding Some General Exact Solutions to the Non-Linear Monge-Ampere Equations (PDEs)

Steve Anglin, Sc.M

Citation :

Steve Anglin, Sc.M, "Finding Some General Exact Solutions to the Non-Linear Monge-Ampere Equations (PDEs)," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 10, pp. 91-97, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I10P513

Abstract

We look at general exact solutions for non-linear Monge-Ampere partial differential equations (PDEs). They are nonlinear elliptic PDEs which typically model surfaces with curvature from differential geometry, optics and other applications of this used by physicists as well as applied and industrial mathematicians.

Keywords

Monge, Ampere, partial, differential equations, PDEs, differential geometry, elliptic, solution, optics, math, applied, calculus

References

[1] Rozhdestvenskii, B. L. and Yanenko, N. N., Systems of Quasilinear Equations and Their Applications to Gas Dynamics, Amer. Math. Society, Providence, 1983.
[2] Khabirov, S. V., Nonisentropic one-dimensional gas motions obtained with the help of the contact group of the nonhomogeneous Monge–Ampere equation, [in Russian], Mat. Sbornik, Vol. 181, No. 12, pp. 1607–1622, 1990.
[3] Ibragimov, N. H. (Editor), CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 1, Symmetries, Exact Solutions and Conservation Laws, CRC Press, Boca Raton, 1994.
[4] Polyanin, A. D. and Zaitsev, V. F., Handbook of Nonlinear Partial Differential Equations , Chapman & Hall/CRC, Boca Raton, 2004.
[5] Goursat, E., A Course of Mathematical Analysis. Vol 3. Part 1 [Russian translation], Gostekhizdat, Moscow, 1933.