Trivially related lax pairs of the Sawada-Kotera equation

Document Type : Research Paper


Sama Technical and Vocational Training College, Islamic Azad university, Urmia Branch, Urmia, Iran.


We show that a recently introduced Lax pair of the Sawada-Kotera equation is not a new one but is trivially related to the known old Lax pair. Using the so-called trivial compositions of the old Lax pairs with a differentially constrained arbitrary operators, we give some examples of trivial Lax pairs of KdV and Sawada-Kotera equations.


Main Subjects

M. Hickman, W. Hereman, J. Larue and U. Göktaş, Scaling invariant Lax pairs of nonlinear evolution equations, Appl. Anal. 91 (2012), no. 2, 381--402.
S. Sakovich, A note on Lax pairs of the Sawada-Kotera equation, J. Math. (2014), Article ID 906165, 4 pages.
P. D. Lax, Integrals of nonlinear equations of evolution and solitary waves, Comm. Pure Appl. Math. 21 (1968) 467--490.
R. K. Dodd and J. D. Gibbon, The prolongation structure of a higher order Korteweg-deVries equation, Proc. R. Soc. Lond. A 358 (1978), no. 1694, 287--296.
K. Sawada and T. Kotera, A method for finding N-soliton solutions of the K.d.V. equation and K.d.V.-like equation, Prog. Theoret. Phys. 51 (1974) 1355--1367.