The integrability of mathematical physics equations is dependent on the consistency of the derivatives of stated functions, according to a study of differential equations. The consistency of derivatives and equations that make up mathematical physics equations revealed that the differential equation is non-integrable in the original coordinate system. To put it another way, the answer isn't a function. If there are any degrees of freedom, however, integrable structures are realised, which are structures on which the derivatives of a differential equation form a differential. Discrete functions are the solutions to mathematical physics equations on integrable systems. This denotes the integrability of the differential equation. The creation of diverse structures such as waves, vortex, and so on is described by double solutions of mathematical physics equations.
L. I. Petrova,
Department of Mathematics and Cybernetics, Faculty of Computational, Lomonosov Moscow State University, Russia.
Please see the link here: https://stm.bookpi.org/NRAMCS-V4/article/view/7029
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