2.6. REFERENCES 47
2.6 REFERENCES
[37] D. J. Arrigo, An Introduction to Partial Differential Equations, Morgan & Claypool, 2017.
9
[38] D. J. Arrigo, Nonclassical contact symmetries and Charpit’s method of compatibility, J.
Nonlinear Math. Phys., 12(3), pp. 321–329, 2005. DOI: 10.2991/jnmp.2005.12.3.1. 18
[39] D. J. Arrigo and L. R. Suazo, First-order compatibility for a (2 C 1)-dimensional dif-
fusion equation, J. Phys. A: Math. Gen., 41, no. 025001, 2008. DOI: 10.1088/1751-
8113/41/2/025001. 38
[40] A. C. Newell and J. A. Whitehead, Finite bandwidth, finite amplitude convection, J. Fluid
Mech., 38(2), pp. 279–303, 1969. DOI: 10.1017/s0022112069000176. 35
[41] L. A. Segel, Distant side-walls cause slow amplitude modulation of cellular convection, J.
Fluid Mech., 38, pp. 203–224, 1969. DOI: 10.1017/s0022112069000127. 35
[42] A. D. Polyanin and V. F. Zaitsev, Exact solutions of the Newell–Whitehead Equation.
http://eqworld.ipmnet.ru 38
[43] E. Pucci and G. Saccomandi, On the weak symmetry groups of partial differential equa-
tions, J. Math. Anal. Appl., 163, pp. 588–598, 1992. DOI: 10.1016/0022-247x(92)90269-j.
45
[44] D. J. Arrigo and J. R. Beckham, Nonclassical symmetries of evolutionary partial dif-
ferential equations and compatibility, J. Math. Anal. Appl., 289, pp. 55–65, 2004. DOI:
10.1016/j.jmaa.2003.08.015. 45
[45] X. Niu, L. Huang, and Z. Pan, e determining equations for the nonclassical
method of the nonlinear differential equation(s) with arbitrary order can be ob-
tained through the compatibility, J. Math. Anal. Appl., 320, pp. 499–509, 2006. DOI:
10.1016/j.jmaa.2005.06.058. 45
[46] G. W. Bluman and J. D. Cole, e general similarity solution of the heat equation, J. Math.
Mech., 18, pp. 1025–1042, 1969. 45
[47] S. Lie, Klassifikation und Integration von gewohnlichen Differentialgleichen zwischen x,
y die eine Gruppe von Transformationen gestatten, Mathematische Annalen, 32, pp. 213–
281, 1888. DOI: 10.1007/bf01444068. 45
[48] D. J. Arrigo, Symmetries Analysis of Differential Equations—An Introduction, Wiley, Hobo-
ken, NJ, 2015. 45
[49] G. Bluman, and S. Kumei, Symmetries and Differential Equations, Springer, Berlin, Ger-
many, 1989. DOI: 10.1007/978-1-4757-4307-4. 45