Estevez–Mansfield–Clarkson equation explained

The Estevez–Mansfield–Clarkson equation is a nonlinear partial differential equation introduced by Pilar Estevez, Elizabeth Mansfield, and Peter Clarkson.^[1]

If U is a function of some other variables x, y, t, then we denote

(\partial ^{3} U)/(\partial t\partial y ^{2}) by U_tyy, and so on. With that notation, the equation isU _{tyyy} + \beta U _{y} U _{yt} + \beta U _{yy} U _{t+U} _{tt} =0

in which

U = u(x,y,t).

References

1. Li Zhibing Traveling Wave Solution of Nonlinear Mathematical Physics equations SCIENCEP 2008(李志斌编著 《非线性数学物理方程的行波解》 页 科学出版社 2008)

1. Graham W. Griffiths William E. Shiesser, Traveling Wave Analysis of Partial Differential Equations, Academy Press
2. Richard H. Enns George C. McCGuire, Nonlinear Physics Birkhauser, 1997
3. Inna Shingareva, Carlos Lizárraga-Celaya, Solving Nonlinear Partial Differential Equations with Maple Springer.
4. Eryk Infeld and George Rowlands, Nonlinear Waves, Solitons and Chaos, Cambridge 2000
5. Saber Elaydi, An Introduction to Difference Equations, Springer 2000
6. Dongming Wang, Elimination Practice, Imperial College Press 2004
7. David Betounes, Partial Differential Equations for Computational Science: With Maple and Vector Analysis, Springer, 1998
8. George Articolo, Partial Differential Equations & Boundary Value Problems with Maple V, Academic Press 1998