Initial value Linear Evolutions equations involving parabolic operator on the plane

Gadagkar P.V.

doi:https://doi.org/10.14445/22315373/IJMTT-V47P546

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 47 | Number 5 | Year 2017 | Article Id. IJMTT-V47P546 | DOI : https://doi.org/10.14445/22315373/IJMTT-V47P546

Initial value Linear Evolutions equations involving parabolic operator on the plane

Gadagkar P.V.

Citation :

Gadagkar P.V., "Initial value Linear Evolutions equations involving parabolic operator on the plane," International Journal of Mathematics Trends and Technology (IJMTT), vol. 47, no. 5, pp. 336-337, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V47P546

Abstract

A unique solution of an initial value problem involving a parabolic operator on the plane of linear evolution equations is obtained by constructing its Lax pair and performing spectral analysis.

Keywords

Lax pair, evolution equation.

References

1. P.D. Lax , Commun. Pure Appl., (1968), 21, 467.
2. A.S. Fokas, On the integrability of linear and nonlinear partial differential equations, Journal of Mathematical Physics, (2000), 41, 4188-4237.
3. M.J. Ablowitz and A.S. Fokas, Introduction and Applications of Complex Variables (Cambridge University Press, Cambridge, UK, 1997).