Dr. Denys Dutykh✓ Add us as a preferred source on Google

Mastodon @denys@mathstodon.xyz

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Known for

$A question about solitary waves to test your intuition before I show what we found. The family of long-wave equations \[ u_t - u_{xxt} = -u_x - u\,u_x + \alpha\,(u\,u_{xxx} + 2u_x u_{xx}) \] contains the Benjamin-Bona-Mahony (BBM) equation of 1972 at $\alpha = 0$. Every member has solitary waves $u(x - ct)$, and in every member the crest of such a wave has height $3(c-1)$, whatever $\alpha\$ 3 views A question about solitary waves to test your intuition before I show what we found. The family of long-wave equations \[ u_t - u_{xxt} = -u_x - u\,u_x + \alpha\,(u\,u_{xxx} + 2u_x u_{xx}) \] contains the Benjamin-Bona-Mahony (BBM) equation of 1972 at \(\alpha = 0$. Every member has solitary waves $u(x - ct)$, and in every member the crest of such a wave has height $3(c-1)$, whatever \(\alpha\

Hello again, Mathstodon. A week ago I said who I am; today I would like to say what you will find here.
I am an applied mathematician in Abu Dhabi. My work moves between water waves and tsunamis, solitons, numerical methods for partial differential equations, black holes that ring after a merger, and lately Markov numbers. What I enjoy most is the moment when a classical piece of pure mathematics

1 views Hello again, Mathstodon. A week ago I said who I am; today I would like to say what you will find here. I am an applied mathematician in Abu Dhabi. My work moves between water waves and tsunamis, solitons, numerical methods for partial differential equations, black holes that ring after a merger, and lately Markov numbers. What I enjoy most is the moment when a classical piece of pure mathematics

📊 Post engagement

Avg engagement / post

33.3%

Engagement vs followers

Oct 2026

On Mastodon since

🔥 Top post: Hello Mathstodon! I’m Denys Dutykh, an applied mathematician at · 10 likes + reposts

📊 Activity & format

Posting cadence

6 / week

Posts several times a week.

Content mix

Mostly images

Recent: 1 text · 5 image · 0 video.

Follower / following

0.3×

Follows 59 back. A more reciprocal / networked account.

🐘 Community & instance

Home server

mathstodon.xyz

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✅ Link-verified

Verified link

Proved ownership of a website linked on their profile — Mastodon's green-check verification, a real identity signal rather than a paid badge.

On Mastodon since

Oct 2026

An established account with real history on the platform.

💡 Facts

🗓️Joined Mastodon in 2026.

👁️Averages 5 views per post.

📤Posts about 6× per week.

🕵️ Fake follower check

Estimated

68/100

Good Credibility score

85%

Real Real audience

Low Fake-follower risk

Medium Data confidence

Est. 85% real, active audience · Low fake-follower risk.
Strong engagement (~0.3× of followers engage each post) — an active, real audience.
Verified account.
Very new account (under 3 months) — higher throwaway/bot risk.

Heuristic estimate from engagement, follower ratios, account age & growth — a screening signal, not a guarantee.

About

Applied mathematician at Khalifa University, Abu Dhabi. I work on nonlinear waves and tsunamis, solitons, numerical methods for PDEs and black holes that ring, and lately on Markov numbers. Here I post one mathematical object at a time from my research, with a picture and a question: the places where pure mathematics turns up inside applied problems.

📸 Gallery

$Why $1/3$? Write $u(x,t) = w(x + t/2,\, t/3) - 3/2$. The member $\alpha = 1/3$ becomes the Camassa-Holm equation of 1993, \[ m_t + w\,m_x + 2w_x\,m = 0, \qquad m = w - w_{xx}, \] a classic integrable model of water waves, so its clean collisions are no surprise once one sees the change of variables. In 2021, a computer-aided Lie symmetry analysis with Alexei Cheviakov and Aidar Assylbekuly h$ $The same collision in space and time, in the frame that moves at the mean speed 1.25 of the two waves, with the colour showing $|u|$ on a logarithmic scale from $10^{-14}$ to 1. The two waves cross at $t \approx 500$. For BBM the crossing sheds a fan of small waves, which run backwards in this frame, wrap around the periodic channel and soon fill it at the level of $10^{-4}$ to $10^{-6}$$ $The answer is $\alpha = 1/3$. We let the tall wave overtake the small one in 57 members of the family, from $\alpha = 0$ to $\alpha = 1$, up to $t = 1000$, then subtracted the two solitary waves and measured what was left. BBM keeps ripples of $2.5 \times 10^{-4}$, the member $\alpha = 1$ ripples of $9 \times 10^{-3}$. At $\alpha = 1/3$ the remainder is $2 \times 10^{-13}$, the r$ $A question about solitary waves to test your intuition before I show what we found. The family of long-wave equations \[ u_t - u_{xxt} = -u_x - u\,u_x + \alpha\,(u\,u_{xxx} + 2u_x u_{xx}) \] contains the Benjamin-Bona-Mahony (BBM) equation of 1972 at $\alpha = 0$. Every member has solitary waves $u(x - ct)$, and in every member the crest of such a wave has height $3(c-1)$, whatever \(\alpha\$

🔀 Audience overlap

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