The head of the Department of Applied Mathematics at MEPhI, Professor Nikolai Kudryashov, solved the problem of constructing a family of equations of arbitrary order with a complex nonlinear refractive index. This will help solve the actual problem of information transmission in a nonlinear medium via optical communication lines. The results of the study were published in Applied Mathematics Letters.

Today, according to researchers, one of the main problems of information transmission through optical communication channels is the construction of an adequate model that takes into account the main physical processes in a nonlinear medium.

Exactly fifty years ago, theoretical scientists suggested that such information transfer is possible using the so-called "optical solitons" - solitary pulses propagating in a nonlinear medium at a constant speed and without changing shape.

“In reality, due to the processes of energy dissipation, the impulses still change. But at a certain period of time and for certain distances, the main mechanisms, nevertheless, play a decisive role in the transmission of information,” said Nikolai Kudryashov.

The existence of optical solitons, according to him, was experimentally confirmed in 1980, which served as a powerful impetus for the development of nonlinear optics.

Nikolai Kudryashov noted that at present several mathematical models are known in nonlinear optics, which are used to describe the propagation of optical pulses in an optical fiber. As a rule, these mathematical models contain several small-order derivatives responsible for dispersion processes, and several degrees of nonlinearity that characterize the refractive indices of a nonlinear medium.

“Mathematical models with higher-order derivatives and more complex dependences of the refractive index of a medium describe the processes of pulse propagation in an optical medium more accurately, but make it difficult to use numerical methods in mathematical modeling. I managed to pose and solve the problem of constructing a family of equations of an arbitrary order with a complex nonlinear refractive index that has two types of soliton solutions in the form of light and nested solitons,” the scientist said.

He noted that the study expands knowledge about the processes occurring in nonlinear optics and provides additional understanding of the nonlinear mathematical models used to describe the propagation of pulses in an optical medium.

“The paper shows that a mathematical model described by a partial differential equation of an arbitrary order, and with a complex nonlinear dependence of the refractive index, can also have soliton solutions that can occur in a nonlinear medium,” Nikolai Kudryashov explained.

It is expected that the new mathematical model proposed by the MEPhI scientist will be able to more adequately and reliably describe the experimental features in the transmission of information in optical communication lines in the future.

  Honored Scientist of the Russian Federation, laureate of the State Prize of the USSR, laureate of the Prize of the Government of the Russian Federation Nikolai Kudryashov is today the most cited scientist at MEPhI, included in the annual ranking of the most cited scientists in the world by the number of mentions in Scopus (https://elsevier.digitalcommonsdata.com/datasets/btchxktzyw/4).