The beauty of equations and the romance of nonlinear physics

Translation. Region: Russian Federation –

Source: Novosibirsk State University –

An important disclaimer is at the bottom of this article.

Before the New Year holidays, an auditorium named after the eminent Russian theoretical physicist Vladimir Evgenievich Zakharov opened in the NSU auditorium building, which is part of the second phase of the new campus being built as part of the national project "Youth and Children." Following the ceremony dedicated to this memorable event for the university, former NSU Rector, Doctor of Physics and Mathematics, and Academician of the Russian Academy of Sciences Mikhail Fedoruk shared his memories of this remarkable man, a brilliant scientist, a talented mentor to young scientists, and an outstanding poet.

Vladimir Zakharov's name was etched into NSU's history at the very beginning of his scientific career, when the young scientist became one of its first graduates. NSU's first graduating class was in December 1963. Sixty-six specialists received diplomas from the young university: 26 physicists, 24 mathematicians, and 10 mechanics specialists. They had transferred from other universities but completed their studies and defended their theses at NSU. Among the first graduates, in addition to Vladimir Zakharov, were A. A. Galeev, A. M. Fridman, and Yu. L. Ershov, who later became academicians of the Russian Academy of Sciences.

Mikhail Petrovich, you worked with Vladimir Evgenievich for a long time. What do you remember about him?

I wasn't Vladimir Evgenievich's direct student, but we spent a lot of time together over the last 13 years of his life, and he supported me when I was elected rector of NSU. He was a very interesting person, gifted with remarkable talent in everything he did. Take, for example, the equations you can see next to his portrait on the wall of the lecture hall named after him. If you delve into even one equation in Lax's formulation, it becomes clear that only a genius could have come up with such a thing. This equation pertains to the theory of nonlinear integrable systems and is key to describing solitons in nonlinear optics (the propagation of light in a medium) or in hydrodynamics (water waves). It is closely related to the Lax representation, which allows a complex nonlinear equation to be reduced to a system of linear problems, making it solvable using the inverse scattering method.

In addition to being a great scientist, Vladimir Evgenievich was a very talented and renowned poet. That's why, in the lecture hall named after him, his poem "Theorist," written in 1980, is displayed on the same wall as the formulas. This is my favorite poem by Vladimir Evgenievich. It's quite bold, if you read the lines carefully. I believe this man's literary legacy should not be forgotten; his works should be revisited and understood, because their lines remain relevant today. I carefully preserve his small collection of six volumes of his works in my home library. The first volume contains his inscription addressed to me with very warm wishes. For me, the opening of this lecture hall is a tribute to the memory of this remarkable and amazingly talented person, and I am glad that it is adorned with lines from my favorite poem by Vladimir Evgenievich. Current NSU students should know what remarkable and talented people our university has produced.

Vladimir Evgenievich was a man of remarkable civic commitment. While working at NSU, he signed the famous "Letter of Forty-Six." And he didn't just sign it—the signing took place in his apartment. As a reminder, the "Letter of Forty-Six" was signed on February 19, 1968, by forty-six academic staff members at Akademgorodok. It protested the violations of the law at the Moscow trial of the "Four," namely, samizdat activists and human rights defenders Alexander Ginzburg, Yuri Galanskov, Alexei Dobrovolsky, and Vera Lashkova, who were arrested in January 1967 on charges of anti-Soviet agitation and propaganda. Their trial took place in January 1968, and all four were sentenced to varying terms of imprisonment. The "Letter of Forty-Six" was sent to the Supreme Court of the RSFSR and the Prosecutor General of the USSR, with copies to the Chairman of the Presidium of the Supreme Soviet of the USSR N.V. Podgorny, the General Secretary of the Central Committee of the CPSU L.I. Brezhnev, the Chairman of the Council of Ministers of the USSR A.N. Kosygin, and the editorial office of the newspaper Komsomolskaya Pravda.

After moving to Moscow, Vladimir Evgenievich served as director of the Landau Institute for Theoretical Physics for ten years. He succeeded the institute's first director, Academician of the USSR Academy of Sciences Isaak Markovich Khalatnikov. Incidentally, the institute has had only four directors in its history, including its current director, Igor Valentinovich Kolokolov, who, like Vladimir Evgenievich, is a graduate of the Physics Department of Novosibirsk State University.

Vladimir Evgenievich's fight against pseudoscience is also significant, demonstrating integrity, courage, and tenacity. He demonstrated these qualities in everything and always, including by refusing the Lenin Prize for developing the inverse scattering method. Initially, it was decided to award this prize to Vladimir Evgenievich, Alexey Borisovich Shabat, and Ludwig Dmitrievich Faddeev. However, Alexey Vladimirovich Shabat's name was removed from the list for various reasons, and his colleagues then declined to accept this prestigious award. At that time, this was a very bold decision, one that few would have dared to make.

He took another very bold step when he became one of the organizers of the informal "July 1st" Club, which united leading Russian scientists who opposed the 2013 reform of the Russian Academy of Sciences.

Throughout his life, Vladimir Evgenievich Zakharov showed himself to be a principled, honest, fair and highly moral person.

— It is known that Vladimir Evgenievich had a very high h-index—65. Tell us about his contribution to science?

"Even now, my scientific work is connected to the contributions Vladimir Evgenievich made. First and foremost, of course, is the theory of wave collapses, which was formulated here in the Novosibirsk Akademgorodok in the early 1970s."

His second significant discovery was the development of the inverse scattering method and the construction of multisoliton solutions within the framework of the nonlinear Schrödinger equation, which you can see on the wall of the lecture hall named after him. It is undoubtedly a gem of 20th-century theoretical and mathematical physics. I'll try to explain it as simply as possible: there is a linear Fourier transform. A group of scientists, including Vladimir Evgenievich, constructed a nonlinear Fourier transform in which the spectral data contains not only a continuous spectrum but also a discrete one. The greatest achievement of Vladimir Evgenievich and Anatoly Borisovich Shabat is their discovery of the Lax pair for the nonlinear Schrödinger equation. I'm still amazed at how they managed it! Vladimir Evgenievich once told Sergei Turitsyn and me that he spent a year and a half thinking about this problem, but I'm sure that ordinary people would have spent 150 years pondering this problem, and it's not a given that they would have found a solution.

His third major achievement is wave turbulence. These are the spectra now called Zakharov-Kolmogorov spectra, and the discovery of the inverse cascade. It was for this discovery that Vladimir Evgenievich was awarded the Dirac Medal, which is not awarded to Nobel laureates. True, he never received the Nobel Prize, although he undoubtedly deserved it. Unfortunately, almost all the creators of nonlinear theory have already passed away. And, of course, there are very few people left of Academician Zakharov's stature.

— What contribution do you think Vladimir Evgenievich made to the development of NSU?

"I consider Vladimir Evgenievich one of our university's most outstanding alumni. NSU has produced many outstanding, talented scientists who have made invaluable contributions to science, but even if he were the only one, that would fully justify the university's existence from its founding to the present day."

While teaching at NSU, Vladimir Evgenievich wasn't shy about admitting his mistakes when they occurred, showed his students how to correct them, and taught them to think from a research perspective. He believed that this was the only way to cultivate a scientist. And this, in my opinion, is his most important contribution to teaching.

Returning to Novosibirsk in 2010, he founded the Laboratory of Nonlinear Wave Processes at NSU. It's worth noting that much earlier, he had given impetus to the development of nonlinear science. He recounted that during his student years, the 10-volume theoretical physics textbook by L. D. Landau and E. M. Lifshitz was the standard textbook for physicists. This course was missing only one volume devoted to nonlinear science. Vladimir Evgenievich was one of the founders of this field. And now, at NSU, we strive to continue his life's work.

— It would seem that there are no concepts more distant from each other than physics and poetry, but Vladimir Evgenievich managed to demonstrate through his own example that this is not so…

"I think physics is very romantic. Our university was founded in 1959, at the height of the debate between physicists and lyricists. Remember Boris Slutsky's poem: "For some reason, physicists are held in high esteem. For some reason, lyricists are relegated. It's not a matter of dry calculations, It's a matter of universal law." Discussions on this matter were published in the Literary Gazette, and our Novosibirsk scientists joined in these debates. Some rushed to justify the lyricists, others to defend the physicists. But in fact, physicists sometimes turned out to be more lyrical than the lyricists themselves. And Vladimir Evgenievich's example confirms this assertion. And this is not surprising, because talented people are talented in many ways. But such people are born very rarely. I would like our students to know what great scientists have graduated from the university. Indeed, by the standards of the Hamburg, Nobel Prize-winning scientists, Vladimir Evgenievich Zakharov is a brilliant scientist. Just look at the beauty of the equations he derived, which are presented to this audience.

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