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# Description of Entire Solutions of Eiconal Type Equations

Published:2011-04-25
Printed: Jun 2012
• Der-Chen Chang,
Department of Mathematics, Georgetown University, Washington, DC 20057 USA
• Bao Qin Li,
Department of Mathematics, Florida International University, Miami, FL 33199 USA
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## Abstract

The paper describes entire solutions to the eiconal type non-linear partial differential equations, which include the eiconal equations $(X_1(u))^2+(X_2(u))^2=1$ as special cases, where $X_1=p_1{\partial}/{\partial z_1}+p_2{\partial}/{\partial z_2}$, $X_2=p_3{\partial}/{\partial z_1}+p_4{\partial}/{\partial z_2}$ are linearly independent operators with $p_j$ being arbitrary polynomials in $\mathbf{C}^2$.
 Keywords: entire solution, eiconal equation, polynomial, transcendental function
 MSC Classifications: 32A15 - Entire functions 35F20 - Nonlinear first-order equations