condition of equations (1) is interpreted as a system of the following partial differential equations of hyperbolic type.
We previously showed that coherent memory determines the extent of system memory and the system proximity to the integrability
limit ([[GAMMA].sub.c] [right arrow] [infinity]) [13, 14].
Mara'beh, "On the linearization of second-order ordinary differential equations to the laguerre form via generalized Sundman transformations," Symmetry, Integrability
and Geometry: Methods and Applications (SIGMA), vol.
Most studies apply the Hirota method to completely integrability
nonlinear problems as in [10, 15-23].
The complete integrability
of (1) was studied by Chowdhury et al.
of various operators and the upper bound estimates for the norms of operators are very important and core topics while studying the [L.sup.p]-theory of differential forms and investigating the qualitative and quantitative properties of the solutions of partial differential equations.
Llibre, "Weierstrass integrability
in Lienard differential systems," Journal of Mathematical Analysis and Applications, vol.
The first point means that solutions to various problems are found in terms of 1-forms and the integrability
properties allow transformation of the solution back to the level of functions.
In particular, the integrability
of J (M is Hermitian) implies the first condition (3.5) and we have to take care of the second condition only.
The Haantjes tensor and double waves for multi-dimensional systems of hydrodynamic type: a necessary condition for integrability
. Proceedings of the Royal Society A, 462:1197-1219, 2006.
Also, it has many qualities such as readability, universality, portability, integrability
, and extensibility.